Samuel Asefa Fufa | Addis Ababa University (original) (raw)

Drafts by Samuel Asefa Fufa

Research paper thumbnail of On Exponential Pointed Structures

In this paper, we use the pointed set partition lattice to introduce exponential pointed structur... more In this paper, we use the pointed set partition lattice to introduce exponential pointed structures which are the pointed analog of exponential structures introduced by Stanley 9. We show that this concept encompasses many examples introduced before. In particular, we introduce pointed decompositions of lattices and study their enumerative and geometric structure. We also show that exponential pointed structures satisfy pointed analogs of Stanley's com-positional and exponential formulas.

Research paper thumbnail of On Combinatorics of Partition Posets Mathematics Subject Classification: 05E11P

We give basic notions concerning partially ordered sets (posets) using the notations of R.P.Stane... more We give basic notions concerning partially ordered sets (posets) using the notations of R.P.Stanely [7]and [10]. We discuss pointed partitions, pointed compositions and knapsack partitions of integers and sets, and we give an overview of the Möbius function of restricted partitions mainly based on the works of Richard Ehrenborg and Margaret A. Readdy. In addition, we refer to [8],[3],and [9] for some concepts to provide a clear summary of the major topics we set out in this project.

Papers by Samuel Asefa Fufa

Research paper thumbnail of Set Partitions and Other Bell Number Enumerated Objects

arXiv (Cornell University), Jan 18, 2021

In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and prese... more In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and present bijections on set partitions. We present a set of permutations whose transposition arrays are the restricted growth functions, thus defining Bell permutations of the second kind. We describe a bijection between Bell permutations of the first kind (introduced by Ponti and Vajnovzski) and the second kind. We present two other Bell number enumerated classes of subexcedant functions. Further, we present bijections on set partitions, in particular, an involution that interchanges the set of merging blocks and the set of successions. We use the bijections to enumerate the distribution of these statistics over the set of set partitions, and also give some enumeration results.

Research paper thumbnail of Distance-Based Topological Descriptors on Ternary Hypertree Networks

Complexity

Topological indices are numeric parameters which portray the topology of a subatomic structure. I... more Topological indices are numeric parameters which portray the topology of a subatomic structure. In QSAR/QSPR analysis, topological descriptors play a vital role to examine the topology of a network. An interconnection network is a structure whose components are connected physically according to some pattern. In this paper, an interconnection network, ternary hypertree, which is a structural combination of complete ternary tree and hypertree, is introduced. We have evaluated the topological descriptors grounded on the distances for the ternary hypertree. The analytical expressions for Wiener, different types of Szeged, and Mostar indices are determined.

Research paper thumbnail of Study of Convexo-Symmetric Networks via Fractional Dimensions

IEEE Access

For having an in-depth study and analysis of various network's structural properties such as inte... more For having an in-depth study and analysis of various network's structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters. Numerous parameters like distance based dimensions help in designing queuing models in restaurants, public health and service facilities and production lines. Likewise, allocations of robots in several production units are indebted to these. Moreover, chemists and druggists use these parameters in finding out new drug type and structural formula of a chemical compound. In this article, we are finding out the extremal values of local fractional metric dimension of a class of network bearing convex as well as symmetric properties known by the name of convex polytopes. Also we have related the significance of our findings towards the end of the manuscript in the form of fire exit plan. The same will serve as a guide for future architects in planning a floor with a conducive fire exit plan. 11 INDEX TERMS Metric dimension, fractional metric dimension, convex polytopes, resolving sets. I. INTRODUCTION 12 A network G comprises of two sets that are V (G) set of ver-13 tices and E(G) the set of objects that forms connection among 14 the nodes/vertices called edges where E(G) ⊆ V (G) × V (G).

Research paper thumbnail of On Topological Analysis of Niobium (II) Oxide Network via Curve Fitting and Entropy Measures

Complexity

The remarkable optical features of metallic nanoparticles have extensively developed the interest... more The remarkable optical features of metallic nanoparticles have extensively developed the interest of scientists and researchers. The generated heat overwhelms cancer tissue incident to nanoparticles with no damage to sound tissues. Niobium nanoparticles have the ability of easy ligands connection so they are very suitable in treating cancer optothermally. A modern field of applied chemistry is chemical graph theory. With the use of combinatorial methods, such as vertex and edge partitions, we explore the connection between atoms and bonds. Topological indices play a vital part in equipping directions to treat cancers or tumors. These indices might be derived experimentally or computed numerically. Although experimental results are worthful but they are expensive as well, so computational analysis provides an economical and rapid way. A topological index is a numerical value that is only determined by the graph. In this paper, we will discuss the chemical graph of niobium (II) oxide....

Research paper thumbnail of On Reverse Valency Based Topological Characterization of a Chemical Compound

Journal of Mathematics

Metal-organic frameworks explicit the consequence of these frameworks with adjustable implementat... more Metal-organic frameworks explicit the consequence of these frameworks with adjustable implementations, namely, energy storage gadgets of magnificent electrode materials, gas store, heterogeneous catalysis, environmental hazard, estimation of chemicals, recognizing of definite gases, controlling solids, and supercapacitors. In this paper, we give explicit expression of the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index, the reverse augmented index, and different types of reverse Zagreb indices of the metal-organic framework M1TPyP-M2 (TPyP = 5, 10, 15, 20-tetrakis (4-pyridyl) porphyrin and M1, M2 = Fe and Co). A graphical comparison of the calculated different types of the reverse degree based topological indices with the aid of the numerical values is also included.

Research paper thumbnail of Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions

IEEE Access

A subset T of the vertex set of a network G is called a resolving set for G if each pair of verti... more A subset T of the vertex set of a network G is called a resolving set for G if each pair of vertices of G have distinct representations with respect to T. A resolving set B among all the resolving sets of a network G is called a fault-tolerant resolving set if B \ {t} is as well a resolving set for each vertex t ∈ B. A fault-tolerant resolving set B of a network G which contains minimum number of vertices is called a faulttolerant metric basis. The cardinality of a fault-tolerant metric basis is called fault-tolerant metric dimension. This concept is widely used to find the integral solution of the problems existing in different disciplines of computer science and chemistry such as linear optimization problems, robot navigation, operation research problems, sensor networking, classification of chemical compounds, drug discoveries, source localization, embedding biological sequence data, detecting network motifs, comparing the interconnected networks and image processing. In this paper, we compute the fault-tolerant metric dimensions of three wheel related networks called by r-level anti-web wheel AWW (n,r) , r-level Helm H (n,r) and r-level anti-web gear AWJ (2n,r) networks in the form of different algebraic expressions consisting of the integral numbers n and r. At the end we discussed a simple method for finding the fault-tolerant metric dimensions and fault-tolerant resolving sets of a r-level wheel related network. We also discussed the importance of these networks in navigation.

Research paper thumbnail of On Degree-Based Topological Indices of Thermodynamic Cuboctahedral Bi-Metallic Structure

Journal of Mathematics

Porous material such as metal-natural constructions and their particular partner metal-natural po... more Porous material such as metal-natural constructions and their particular partner metal-natural poly-hydra are made up of inorganic clusters with no saturation and exhibit great capability for utilization in the absorption of gas and ascending opening in optics and detecting biotechnology and hardware. Cuboctahedral bi-metallic structure is an often-quoted example of metal-natural polyhedra class. In this study, we have calculated the first and second Zagreb index, the augmented Zagreb index, and the inverse Randic, as well as general Randic index, the symmetric division, and harmonic index. We have also discussed these topological indices graphically and have found that the value of almost all indices goes higher and higher as the value of n goes higher.

Research paper thumbnail of On Characterization of Graphs Structures Connected with Some Algebraic Properties

Mathematical Problems in Engineering

In this paper, we have characterized graph structures connected with some algebraic properties. A... more In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops. Also, there is a connection between bipartite graphs and mathematical structures, commutator subloop, associator subloop, and associative part, the nucleus of the loop, through edge labeling.

Research paper thumbnail of Pattern-avoidance and Fuss-Catalan numbers

We study a subset of permutations, where entries are restricted to having the same remainder as t... more We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer kgeq2k \geq 2kgeq2. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations, we recover the Fuss--Catalan numbers. Surprisingly, an analogous statement also holds when we impose the mod kkk restriction on a Catalan family of subexcedant functions. Finally, we completely enumerate all combinations of mod-$k$-alternating permutations, avoiding two patterns of length 3. This is analogous to the systematic study by Simion and Schmidt, of permutations avoiding two patterns of length 3.

Research paper thumbnail of On Neighborhood Degree-Based Topological Analysis of Polyphenylene Network

Mathematical Problems in Engineering, 2022

Organic compounds such as polyphenylene are very important and useful for the synthesis of many n... more Organic compounds such as polyphenylene are very important and useful for the synthesis of many new organic compounds due to their physio-chemical properties. To ascertain these properties, one can use QSPR/QSAR methods which necessitate the computation of topological indices. The topological indices based on two newly introduced abstract notions of ev-degree and ve-degree are in practice to model numerous chemical properties as well as physical properties of organic, inorganic, hybrid, and biological compounds. In this study, we computed a certain number of topological indices for the chemical graph of polyphenylene network which will help to model some of its physio-chemical properties.

Research paper thumbnail of Computation of Metric Dimension of Certain Subdivided Convex Polytopes

Journal of Mathematics, 2022

The distance d z 1 , z 2 from vertex z 1 ∈ V G to z 2 ∈ V G is minimum length of z 1 , z 2 -path ... more The distance d z 1 , z 2 from vertex z 1 ∈ V G to z 2 ∈ V G is minimum length of z 1 , z 2 -path in a given connected graph G having E(G) and V(G) edges and vertices’/nodes’ sets, respectively. Suppose Z = z 1 , z 2 , z 3 , … , z m ⊆ V G is an order set and c ∈ V G , and the code of c with reference to Z is the m-tuple {d(c, z1), d(c, z2), d(c, z13), …, d(c, zk)}. Then, Z is named as the locating set or resolving set if each node of G has unique code. A locating set of least cardinality is described as a basis set for the graph G , and its cardinal number is referred to as metric dimension symbolized by dim G . Metric dimension of certain subdivided convex polytopes S T n has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes.

Research paper thumbnail of On Computation of Entropy Measures and Molecular Descriptors for Isomeric Natural Polymers

Journal of Mathematics, 2022

Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a struct... more Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a structure that is nearly identical to that of amylopectin. It can be found in practically all animal cells and some plant cells. Glycogen is a natural polysaccharide polymer with features that make it a good antiparticle carrier for cancer therapeutics. It is not only biocompatible by nature but also be chemically modified to accommodate additional molecular components. Topological indices are used to create quantitative structure-activity relationships (QSARs), in which the biological activity or other properties of molecules are linked to their chemical structure. We estimated certain K ^ Banhatti and Gourava indices of natural polymers of polysaccharides, namely, glycogen and amylopectin, which have therapeutic applications, extraordinary features, and fascinating molecular framework, in this study. We also discovered some relationships between K ^ Banhatti indices and information entropies...

Research paper thumbnail of On the Möbius Function of a Pointed Graded Lattice

Indian Journal of Pure and Applied Mathematics, 2018

In this paper, we compute the Möbius function of pointed integer partition and pointed ordered se... more In this paper, we compute the Möbius function of pointed integer partition and pointed ordered set partition using topological and analytic methods. We show that the associated order complex is a wedge of spheres and compute the associated reduced homology group for each subposet. In addition, we compute the Möbius function of pointed graded lattice and use our method to compute the Möbius function of pointed direct sum decomposition of vector spaces.

Research paper thumbnail of Degree-Based Molecular Descriptors of Guar Gum and Its Chemical Derivatives

Journal of Chemistry, 2022

The most abundant polycarbonates that are found in food are polysaccharides. A long chain of mono... more The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic index, general Randic index, forgotten index, ABC index, GA index, GH index, Sombor index, and SS index are computed. The chemical derivatives of guar gum such as HPG, CMG, and CMHPG are studied, and topological indices are determined. Finally, numerical and graphical comparison of all the above said ten indices are made for guar gum and its chemical derivatives.

Research paper thumbnail of On Topological Indices for Complex Indium Phosphate Network and Their Applications

Complexity

A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are ... more A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are usually represented as vertices, while their bonding or interaction is shown by edges in a molecular graph. In this paper, we computed various connectivity indices based on degrees of vertices of a chemical graph of indium phosphide (InP). Afterward, we found the physical measures like entropy and heat of formation of InP. Then, we fitted curves between different indices and the thermodynamical properties, namely, heat of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and nonlinearity. Furthermore, we depicted our results numerically and graphically. These numerical systems may give an approach to concentrate on the thermodynamical properties of the compound design of InP at an exceptional level that will help understand the connection between framework measurement and these actions.

Research paper thumbnail of A Review of Enumeration Methods on Integer Partition

Sinet, Ethiopian Journal of Science, 2018

A partition of a non-negative integer is a way of writing as a sum of a non-decreasing sequence... more A partition of a non-negative integer is a way of writing as a sum of a non-decreasing sequence of parts. The paper provides the study of some properties of integer partitions. In particular, we are interested to show the number of partitions of in which the summand appears at most times is equal to the number of partitions in which the part appears any times and the other part appears at most times by using a generating function and algebraic construction.

Research paper thumbnail of Distance Based Indices of Generalized Transformation Graphs

Sinet, Ethiopian Journal of Science, 2019

In this paper, the expressions for the Wiener index, Gutman index, degree distance, eccentric con... more In this paper, the expressions for the Wiener index, Gutman index, degree distance, eccentric connectivity index and eccentric distance sum of the generalized transformation graphs G+-and G -+ are obtained in terms of the parameters of underline graphs.

Research paper thumbnail of On the Möbius Function of A Pointed Graded Lattice

Indian Journal of Pure and Applied Mathematics, 2018

In this paper, we use the pointed set partition lattice to introduce exponential pointed structur... more In this paper, we use the pointed set partition lattice to introduce exponential pointed structures which are the pointed analog of exponential structures introduced by Stanley [3] and new exponential structures from lattices. We show that this concept encompasses many examples introduced before. In particular, we introduce pointed decompositions of lattices and study their enumerative and geometric structure. We also show that exponential pointed structures satisfy pointed analogs of Stanley's compositional and exponential formulas.

Research paper thumbnail of On Exponential Pointed Structures

In this paper, we use the pointed set partition lattice to introduce exponential pointed structur... more In this paper, we use the pointed set partition lattice to introduce exponential pointed structures which are the pointed analog of exponential structures introduced by Stanley 9. We show that this concept encompasses many examples introduced before. In particular, we introduce pointed decompositions of lattices and study their enumerative and geometric structure. We also show that exponential pointed structures satisfy pointed analogs of Stanley's com-positional and exponential formulas.

Research paper thumbnail of On Combinatorics of Partition Posets Mathematics Subject Classification: 05E11P

We give basic notions concerning partially ordered sets (posets) using the notations of R.P.Stane... more We give basic notions concerning partially ordered sets (posets) using the notations of R.P.Stanely [7]and [10]. We discuss pointed partitions, pointed compositions and knapsack partitions of integers and sets, and we give an overview of the Möbius function of restricted partitions mainly based on the works of Richard Ehrenborg and Margaret A. Readdy. In addition, we refer to [8],[3],and [9] for some concepts to provide a clear summary of the major topics we set out in this project.

Research paper thumbnail of Set Partitions and Other Bell Number Enumerated Objects

arXiv (Cornell University), Jan 18, 2021

In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and prese... more In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and present bijections on set partitions. We present a set of permutations whose transposition arrays are the restricted growth functions, thus defining Bell permutations of the second kind. We describe a bijection between Bell permutations of the first kind (introduced by Ponti and Vajnovzski) and the second kind. We present two other Bell number enumerated classes of subexcedant functions. Further, we present bijections on set partitions, in particular, an involution that interchanges the set of merging blocks and the set of successions. We use the bijections to enumerate the distribution of these statistics over the set of set partitions, and also give some enumeration results.

Research paper thumbnail of Distance-Based Topological Descriptors on Ternary Hypertree Networks

Complexity

Topological indices are numeric parameters which portray the topology of a subatomic structure. I... more Topological indices are numeric parameters which portray the topology of a subatomic structure. In QSAR/QSPR analysis, topological descriptors play a vital role to examine the topology of a network. An interconnection network is a structure whose components are connected physically according to some pattern. In this paper, an interconnection network, ternary hypertree, which is a structural combination of complete ternary tree and hypertree, is introduced. We have evaluated the topological descriptors grounded on the distances for the ternary hypertree. The analytical expressions for Wiener, different types of Szeged, and Mostar indices are determined.

Research paper thumbnail of Study of Convexo-Symmetric Networks via Fractional Dimensions

IEEE Access

For having an in-depth study and analysis of various network's structural properties such as inte... more For having an in-depth study and analysis of various network's structural properties such as interconnection, extensibility, availability, centralization, vulnerability and reliability, we require distance based graph theoretic parameters. Numerous parameters like distance based dimensions help in designing queuing models in restaurants, public health and service facilities and production lines. Likewise, allocations of robots in several production units are indebted to these. Moreover, chemists and druggists use these parameters in finding out new drug type and structural formula of a chemical compound. In this article, we are finding out the extremal values of local fractional metric dimension of a class of network bearing convex as well as symmetric properties known by the name of convex polytopes. Also we have related the significance of our findings towards the end of the manuscript in the form of fire exit plan. The same will serve as a guide for future architects in planning a floor with a conducive fire exit plan. 11 INDEX TERMS Metric dimension, fractional metric dimension, convex polytopes, resolving sets. I. INTRODUCTION 12 A network G comprises of two sets that are V (G) set of ver-13 tices and E(G) the set of objects that forms connection among 14 the nodes/vertices called edges where E(G) ⊆ V (G) × V (G).

Research paper thumbnail of On Topological Analysis of Niobium (II) Oxide Network via Curve Fitting and Entropy Measures

Complexity

The remarkable optical features of metallic nanoparticles have extensively developed the interest... more The remarkable optical features of metallic nanoparticles have extensively developed the interest of scientists and researchers. The generated heat overwhelms cancer tissue incident to nanoparticles with no damage to sound tissues. Niobium nanoparticles have the ability of easy ligands connection so they are very suitable in treating cancer optothermally. A modern field of applied chemistry is chemical graph theory. With the use of combinatorial methods, such as vertex and edge partitions, we explore the connection between atoms and bonds. Topological indices play a vital part in equipping directions to treat cancers or tumors. These indices might be derived experimentally or computed numerically. Although experimental results are worthful but they are expensive as well, so computational analysis provides an economical and rapid way. A topological index is a numerical value that is only determined by the graph. In this paper, we will discuss the chemical graph of niobium (II) oxide....

Research paper thumbnail of On Reverse Valency Based Topological Characterization of a Chemical Compound

Journal of Mathematics

Metal-organic frameworks explicit the consequence of these frameworks with adjustable implementat... more Metal-organic frameworks explicit the consequence of these frameworks with adjustable implementations, namely, energy storage gadgets of magnificent electrode materials, gas store, heterogeneous catalysis, environmental hazard, estimation of chemicals, recognizing of definite gases, controlling solids, and supercapacitors. In this paper, we give explicit expression of the reverse general Randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse Balaban index, the reverse augmented index, and different types of reverse Zagreb indices of the metal-organic framework M1TPyP-M2 (TPyP = 5, 10, 15, 20-tetrakis (4-pyridyl) porphyrin and M1, M2 = Fe and Co). A graphical comparison of the calculated different types of the reverse degree based topological indices with the aid of the numerical values is also included.

Research paper thumbnail of Studies of Multilevel Networks via Fault-Tolerant Metric Dimensions

IEEE Access

A subset T of the vertex set of a network G is called a resolving set for G if each pair of verti... more A subset T of the vertex set of a network G is called a resolving set for G if each pair of vertices of G have distinct representations with respect to T. A resolving set B among all the resolving sets of a network G is called a fault-tolerant resolving set if B \ {t} is as well a resolving set for each vertex t ∈ B. A fault-tolerant resolving set B of a network G which contains minimum number of vertices is called a faulttolerant metric basis. The cardinality of a fault-tolerant metric basis is called fault-tolerant metric dimension. This concept is widely used to find the integral solution of the problems existing in different disciplines of computer science and chemistry such as linear optimization problems, robot navigation, operation research problems, sensor networking, classification of chemical compounds, drug discoveries, source localization, embedding biological sequence data, detecting network motifs, comparing the interconnected networks and image processing. In this paper, we compute the fault-tolerant metric dimensions of three wheel related networks called by r-level anti-web wheel AWW (n,r) , r-level Helm H (n,r) and r-level anti-web gear AWJ (2n,r) networks in the form of different algebraic expressions consisting of the integral numbers n and r. At the end we discussed a simple method for finding the fault-tolerant metric dimensions and fault-tolerant resolving sets of a r-level wheel related network. We also discussed the importance of these networks in navigation.

Research paper thumbnail of On Degree-Based Topological Indices of Thermodynamic Cuboctahedral Bi-Metallic Structure

Journal of Mathematics

Porous material such as metal-natural constructions and their particular partner metal-natural po... more Porous material such as metal-natural constructions and their particular partner metal-natural poly-hydra are made up of inorganic clusters with no saturation and exhibit great capability for utilization in the absorption of gas and ascending opening in optics and detecting biotechnology and hardware. Cuboctahedral bi-metallic structure is an often-quoted example of metal-natural polyhedra class. In this study, we have calculated the first and second Zagreb index, the augmented Zagreb index, and the inverse Randic, as well as general Randic index, the symmetric division, and harmonic index. We have also discussed these topological indices graphically and have found that the value of almost all indices goes higher and higher as the value of n goes higher.

Research paper thumbnail of On Characterization of Graphs Structures Connected with Some Algebraic Properties

Mathematical Problems in Engineering

In this paper, we have characterized graph structures connected with some algebraic properties. A... more In this paper, we have characterized graph structures connected with some algebraic properties. Also, this paper is actually the concatenation of graph theory and algebra. We have introduced left and right inverse graphs of antiautomorphic inverse property loops. Also, there is a connection between bipartite graphs and mathematical structures, commutator subloop, associator subloop, and associative part, the nucleus of the loop, through edge labeling.

Research paper thumbnail of Pattern-avoidance and Fuss-Catalan numbers

We study a subset of permutations, where entries are restricted to having the same remainder as t... more We study a subset of permutations, where entries are restricted to having the same remainder as the index, modulo some integer kgeq2k \geq 2kgeq2. We show that when also imposing the classical 132- or 213-avoidance restriction on the permutations, we recover the Fuss--Catalan numbers. Surprisingly, an analogous statement also holds when we impose the mod kkk restriction on a Catalan family of subexcedant functions. Finally, we completely enumerate all combinations of mod-$k$-alternating permutations, avoiding two patterns of length 3. This is analogous to the systematic study by Simion and Schmidt, of permutations avoiding two patterns of length 3.

Research paper thumbnail of On Neighborhood Degree-Based Topological Analysis of Polyphenylene Network

Mathematical Problems in Engineering, 2022

Organic compounds such as polyphenylene are very important and useful for the synthesis of many n... more Organic compounds such as polyphenylene are very important and useful for the synthesis of many new organic compounds due to their physio-chemical properties. To ascertain these properties, one can use QSPR/QSAR methods which necessitate the computation of topological indices. The topological indices based on two newly introduced abstract notions of ev-degree and ve-degree are in practice to model numerous chemical properties as well as physical properties of organic, inorganic, hybrid, and biological compounds. In this study, we computed a certain number of topological indices for the chemical graph of polyphenylene network which will help to model some of its physio-chemical properties.

Research paper thumbnail of Computation of Metric Dimension of Certain Subdivided Convex Polytopes

Journal of Mathematics, 2022

The distance d z 1 , z 2 from vertex z 1 ∈ V G to z 2 ∈ V G is minimum length of z 1 , z 2 -path ... more The distance d z 1 , z 2 from vertex z 1 ∈ V G to z 2 ∈ V G is minimum length of z 1 , z 2 -path in a given connected graph G having E(G) and V(G) edges and vertices’/nodes’ sets, respectively. Suppose Z = z 1 , z 2 , z 3 , … , z m ⊆ V G is an order set and c ∈ V G , and the code of c with reference to Z is the m-tuple {d(c, z1), d(c, z2), d(c, z13), …, d(c, zk)}. Then, Z is named as the locating set or resolving set if each node of G has unique code. A locating set of least cardinality is described as a basis set for the graph G , and its cardinal number is referred to as metric dimension symbolized by dim G . Metric dimension of certain subdivided convex polytopes S T n has been computed, and it is concluded that just four vertices are sufficient for unique coding of all nodes belonging to this family of convex polytopes.

Research paper thumbnail of On Computation of Entropy Measures and Molecular Descriptors for Isomeric Natural Polymers

Journal of Mathematics, 2022

Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a struct... more Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a structure that is nearly identical to that of amylopectin. It can be found in practically all animal cells and some plant cells. Glycogen is a natural polysaccharide polymer with features that make it a good antiparticle carrier for cancer therapeutics. It is not only biocompatible by nature but also be chemically modified to accommodate additional molecular components. Topological indices are used to create quantitative structure-activity relationships (QSARs), in which the biological activity or other properties of molecules are linked to their chemical structure. We estimated certain K ^ Banhatti and Gourava indices of natural polymers of polysaccharides, namely, glycogen and amylopectin, which have therapeutic applications, extraordinary features, and fascinating molecular framework, in this study. We also discovered some relationships between K ^ Banhatti indices and information entropies...

Research paper thumbnail of On the Möbius Function of a Pointed Graded Lattice

Indian Journal of Pure and Applied Mathematics, 2018

In this paper, we compute the Möbius function of pointed integer partition and pointed ordered se... more In this paper, we compute the Möbius function of pointed integer partition and pointed ordered set partition using topological and analytic methods. We show that the associated order complex is a wedge of spheres and compute the associated reduced homology group for each subposet. In addition, we compute the Möbius function of pointed graded lattice and use our method to compute the Möbius function of pointed direct sum decomposition of vector spaces.

Research paper thumbnail of Degree-Based Molecular Descriptors of Guar Gum and Its Chemical Derivatives

Journal of Chemistry, 2022

The most abundant polycarbonates that are found in food are polysaccharides. A long chain of mono... more The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic index, general Randic index, forgotten index, ABC index, GA index, GH index, Sombor index, and SS index are computed. The chemical derivatives of guar gum such as HPG, CMG, and CMHPG are studied, and topological indices are determined. Finally, numerical and graphical comparison of all the above said ten indices are made for guar gum and its chemical derivatives.

Research paper thumbnail of On Topological Indices for Complex Indium Phosphate Network and Their Applications

Complexity

A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are ... more A chemical compound in the form of graph terminology is known as a chemical graph. Molecules are usually represented as vertices, while their bonding or interaction is shown by edges in a molecular graph. In this paper, we computed various connectivity indices based on degrees of vertices of a chemical graph of indium phosphide (InP). Afterward, we found the physical measures like entropy and heat of formation of InP. Then, we fitted curves between different indices and the thermodynamical properties, namely, heat of formation and entropy. Curve fitting was done in MATLAB through different methods based on linearity and nonlinearity. Furthermore, we depicted our results numerically and graphically. These numerical systems may give an approach to concentrate on the thermodynamical properties of the compound design of InP at an exceptional level that will help understand the connection between framework measurement and these actions.

Research paper thumbnail of A Review of Enumeration Methods on Integer Partition

Sinet, Ethiopian Journal of Science, 2018

A partition of a non-negative integer is a way of writing as a sum of a non-decreasing sequence... more A partition of a non-negative integer is a way of writing as a sum of a non-decreasing sequence of parts. The paper provides the study of some properties of integer partitions. In particular, we are interested to show the number of partitions of in which the summand appears at most times is equal to the number of partitions in which the part appears any times and the other part appears at most times by using a generating function and algebraic construction.

Research paper thumbnail of Distance Based Indices of Generalized Transformation Graphs

Sinet, Ethiopian Journal of Science, 2019

In this paper, the expressions for the Wiener index, Gutman index, degree distance, eccentric con... more In this paper, the expressions for the Wiener index, Gutman index, degree distance, eccentric connectivity index and eccentric distance sum of the generalized transformation graphs G+-and G -+ are obtained in terms of the parameters of underline graphs.

Research paper thumbnail of On the Möbius Function of A Pointed Graded Lattice

Indian Journal of Pure and Applied Mathematics, 2018

In this paper, we use the pointed set partition lattice to introduce exponential pointed structur... more In this paper, we use the pointed set partition lattice to introduce exponential pointed structures which are the pointed analog of exponential structures introduced by Stanley [3] and new exponential structures from lattices. We show that this concept encompasses many examples introduced before. In particular, we introduce pointed decompositions of lattices and study their enumerative and geometric structure. We also show that exponential pointed structures satisfy pointed analogs of Stanley's compositional and exponential formulas.

Research paper thumbnail of Shellability of Pointed Integer Partition

Acta Mechanica Slovaca, Dec 17, 2019

In this paper we study, pointed integer partition defined as a pair

Research paper thumbnail of Distance-Based Indices of Complete m-Ary Trees

Discrete Mathematics, Algorithms and Applications

Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer sc... more Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer science and chemistry. We present exact values of all important distance-based indices for complete [Formula: see text]-ary trees. We solve recurrence relations to obtain the value of the most well-known index called the Wiener index. New methods are used to express the other indices (the degree distance, the eccentric distance sum, the Gutman index, the edge-Wiener index, the hyper-Wiener index and the edge-hyper-Wiener index) as well. Values of distance-based indices for complete binary trees are corollaries of the main results.