Mehdi Alaeiyan - Academia.edu (original) (raw)
Papers by Mehdi Alaeiyan
The perfect m-coloring with matrix A = [a ij ] i,j∈{1,...,m} of a graph G = (V, E) with {1,. .. ,... more The perfect m-coloring with matrix A = [a ij ] i,j∈{1,...,m} of a graph G = (V, E) with {1,. .. , m} color is a vertices coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is a ij , independent of the choice of vertex in color i. The matrix A = [a ij ] i,j∈{1,...,m} is called the parameter matrix. We study the perfect 4-colorings of the 3-regular graphs of order 10, that is, we determine a list of all color parameter matrices corresponding to perfect colorings of 3-regular graphs of order 10.
Journal of Mathematical Extension, Sep 6, 2021
The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · ... more The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · , m} color is a vertex coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent from the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,··· ,m} is called the parameter matrix. We study the perfect 4-coloring of the 3-regular graphs of order at Most 8, that is, we determine a list of all color parameter matrices corresponding to perfect coloring of 3-regular graphs of order 4, 6 and 8.
Eurasian chemical communications, Aug 1, 2020
Computing topological indices of drug structures provides the chemical information about the unde... more Computing topological indices of drug structures provides the chemical information about the underlying topology of the drug's structures. Novel anticancer drug studies have been conducting by researches to design and produce ideal drugs. Chemical properties of these new drug candidates investigated using the simulation methods. Topological indices also have been used to investigate the chemical properties of some drug structures. Ve-degree and Ev-degree topological indices have been defined recently in chemical graph theory. In this study we evaluated the ev-degree and ve-degree topological indices of some newly defined anticancer drug candidates which are based on alkylating agent.
Advances in Materials Science and Engineering, Jun 23, 2019
In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for ato... more In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometricarithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.
Journal of Discrete Mathematical Sciences and Cryptography, Jun 20, 2022
Journal of Discrete Mathematical Sciences and Cryptography, May 15, 2022
Journal of Computational and Theoretical Nanoscience, Apr 1, 2015
ABSTRACT A topological index is a numeric quantity of a molecule that is mathematically derived i... more ABSTRACT A topological index is a numeric quantity of a molecule that is mathematically derived in unambiguous way from the structural graph of a molecule. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biolog-ical and other properties of chemical compounds. In this paer, the most important topological index called “fifth geometric-arithmetic index” of H-Naphtalenic Nanosheet [4n, 2m] is computed for first time.
Journal of Information and Optimization Sciences, May 18, 2020
For connected graph G, the neighbourhood polynomial is defined as
DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2008
We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G ... more We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6.
Journal of the Indonesian Mathematical Society, Apr 28, 2012
A graph is said to be semisymmetric if its full automorphism group acts transitively on its edge ... more A graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we prove that there is only one semisymmetric cubic graph of order 28p 2 , where p is a prime.
DergiPark (Istanbul University), Feb 1, 2012
A graph is called edge-transitive if its automorphism group acts transitively on its set of edges... more A graph is called edge-transitive if its automorphism group acts transitively on its set of edges. In this paper we classify all connected cubic edge-transitive graphs of order 14p 2 , where p is a prime.
Journal of Mathematics, Jun 15, 2021
A dendrimer is an artificially manufactured or synthesized molecule built up from branched units ... more A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In mathematical chemistry, a particular attention is given to degree-based graph invariant. e Narumi-Katayama index and its modified Narumi-Katayama index of a graph G denoted by NK (G) and NK * (G) are equal to the product of the degrees of the vertices of G. In this paper, we calculate the Narumi-Katayama Index and modified Narumi-Katayama index for some families of dendrimers.
Eurasian Chemical Communications, Mar 11, 2020
Mathematical chemistry is the area of research engaged in new application of Mathematics in Chemi... more Mathematical chemistry is the area of research engaged in new application of Mathematics in Chemistry. Major areas of research in mathematical chemistry include chemical graph theory. Chemical graph theory applies graph theory to mathematical modeling of chemical phenomena. If G=(V(G),E(G)) is a connected graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, then the eccentric connectivity index of G (denoted by ξ(G)) was defined as ζ(G)=
Mathematical Biosciences and Engineering
The use of topological descriptors is the key method, regardless of great advances taking place i... more The use of topological descriptors is the key method, regardless of great advances taking place in the field of drug design. Descriptors portray the chemical characteristic of a molecule in numerical form, that is used for QSAR/QSPR models. The numerical values related with chemical constitutions that correlate the chemical structure with the physical properties refer to topological indices. The study of chemical structure with chemical reactivity or biological activity is termed quantitative structure activity relationship, in which topological index plays a significant role. Chemical graph theory is one such significant branch of science which plays a key role in QSAR/QSPR/QSTR studies. This work is focused on computing various degree-based topological indices and regression model of nine anti-malaria drugs. Regression models are fitted for computed indices values with 6 physicochemical properties of the anti-malaria drugs are studied. Based on the results obtained, an analysis is...
Journal of Discrete Mathematical Sciences and Cryptography
Abstract Irregularity indices are a special type of topological indices, first studied by Paul Er... more Abstract Irregularity indices are a special type of topological indices, first studied by Paul Erdös In this paper, we compute twelve degree-based irregularity topological indices for some networks like Butterfly networks, BF(r), Benes networks B(r), two important mesh derived networks namely MDN1, MDN2 with respect to the edge partition obtained for each such networks.
Journal of Discrete Mathematical Sciences and Cryptography
Abstract Topological indices are numerical parameters associated with underlying topology of a mo... more Abstract Topological indices are numerical parameters associated with underlying topology of a molecular structure. They are correlated with several physio-chemical properties of chemical compounds. Recently, Euclidean metric based topological index has been introduced named as Sombor index. Therefore, in this article, we will discuss combinatorial aspects and compute Sombor index, average Sombor index and the reduced Sombor index of line graph of silicate carbides Si 2 C 3 -I[p, q].
Journal of Information and Optimization Sciences, 2020
Mathematical topological characterization of chemical graphs gives information about some physica... more Mathematical topological characterization of chemical graphs gives information about some physical properties of molecules. Classical degree based topological indices of copper oxide have been recently calculated. Ve-degree and Ev-degree based topological indices have been newly defined in graph theory. In this study we investigate ve-degree topological properties of copper oxide. We calculate ve-degree Zagreb and Randić indices of copper oxide.
Journal of Discrete Mathematical Sciences and Cryptography, 2020
A topological index is a real number which is same under graph isomorphism and it is derived from... more A topological index is a real number which is same under graph isomorphism and it is derived from a graph by mathematically. In chemical graph theory, a molecular graph is a simple graph having no loops and multiple edges in which atoms and chemical bonds are represented by vertices and edges respectively. Topological indices defined on these chemical molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. In this paper, we compute general expressions
Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer... more Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as m:=move(G):=sup Γ {|Γ g ∖Γ|∣g∈G}. Let p be a prime, p≥5, and let move(G)=m. If G is a 2-group on each orbit, and p is the least odd prime dividing |G|, then n:=|Ω|≤p p-1(⌊2mp p-1⌋-1). Moreover, for an infinite family of groups the above bound is attained.
A regular graph G is said to be semisymmetric if its full automorphism group acts transitively on... more A regular graph G is said to be semisymmetric if its full automorphism group acts transitively on its edge-set but not on its vertex-set. It was shown by Folkman [5] that a regular edge-transitive graph of order 2 p or 2 p 2 is necessarily vertex-transitive, where p is a prime. In this paper, it is proved that there is no connected semisymmetric cubic graph of order 4 p 2, where p is a prime.
The perfect m-coloring with matrix A = [a ij ] i,j∈{1,...,m} of a graph G = (V, E) with {1,. .. ,... more The perfect m-coloring with matrix A = [a ij ] i,j∈{1,...,m} of a graph G = (V, E) with {1,. .. , m} color is a vertices coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is a ij , independent of the choice of vertex in color i. The matrix A = [a ij ] i,j∈{1,...,m} is called the parameter matrix. We study the perfect 4-colorings of the 3-regular graphs of order 10, that is, we determine a list of all color parameter matrices corresponding to perfect colorings of 3-regular graphs of order 10.
Journal of Mathematical Extension, Sep 6, 2021
The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · ... more The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · , m} color is a vertex coloring of G with m-color so that number of vertex in color j adjacent to a fixed vertex in color i is aij , independent from the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,··· ,m} is called the parameter matrix. We study the perfect 4-coloring of the 3-regular graphs of order at Most 8, that is, we determine a list of all color parameter matrices corresponding to perfect coloring of 3-regular graphs of order 4, 6 and 8.
Eurasian chemical communications, Aug 1, 2020
Computing topological indices of drug structures provides the chemical information about the unde... more Computing topological indices of drug structures provides the chemical information about the underlying topology of the drug's structures. Novel anticancer drug studies have been conducting by researches to design and produce ideal drugs. Chemical properties of these new drug candidates investigated using the simulation methods. Topological indices also have been used to investigate the chemical properties of some drug structures. Ve-degree and Ev-degree topological indices have been defined recently in chemical graph theory. In this study we evaluated the ev-degree and ve-degree topological indices of some newly defined anticancer drug candidates which are based on alkylating agent.
Advances in Materials Science and Engineering, Jun 23, 2019
In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for ato... more In this paper, we computed the topological indices of pent-heptagonal nanosheet. Formulas for atom-bond connectivity index, fourth atom-bond connectivity index, Randić connectivity index, sum-connectivity index, first Zagreb index, second Zagreb index, augmented Zagreb index, modified Zagreb index, hyper Zagreb index, geometric-arithmetic index, fifth geometricarithmetic index, Sanskruti index, forgotten index, and harmonic index of pent-heptagonal nanosheet have been derived.
Journal of Discrete Mathematical Sciences and Cryptography, Jun 20, 2022
Journal of Discrete Mathematical Sciences and Cryptography, May 15, 2022
Journal of Computational and Theoretical Nanoscience, Apr 1, 2015
ABSTRACT A topological index is a numeric quantity of a molecule that is mathematically derived i... more ABSTRACT A topological index is a numeric quantity of a molecule that is mathematically derived in unambiguous way from the structural graph of a molecule. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biolog-ical and other properties of chemical compounds. In this paer, the most important topological index called “fifth geometric-arithmetic index” of H-Naphtalenic Nanosheet [4n, 2m] is computed for first time.
Journal of Information and Optimization Sciences, May 18, 2020
For connected graph G, the neighbourhood polynomial is defined as
DOAJ (DOAJ: Directory of Open Access Journals), Mar 1, 2008
We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G ... more We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6.
Journal of the Indonesian Mathematical Society, Apr 28, 2012
A graph is said to be semisymmetric if its full automorphism group acts transitively on its edge ... more A graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we prove that there is only one semisymmetric cubic graph of order 28p 2 , where p is a prime.
DergiPark (Istanbul University), Feb 1, 2012
A graph is called edge-transitive if its automorphism group acts transitively on its set of edges... more A graph is called edge-transitive if its automorphism group acts transitively on its set of edges. In this paper we classify all connected cubic edge-transitive graphs of order 14p 2 , where p is a prime.
Journal of Mathematics, Jun 15, 2021
A dendrimer is an artificially manufactured or synthesized molecule built up from branched units ... more A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In mathematical chemistry, a particular attention is given to degree-based graph invariant. e Narumi-Katayama index and its modified Narumi-Katayama index of a graph G denoted by NK (G) and NK * (G) are equal to the product of the degrees of the vertices of G. In this paper, we calculate the Narumi-Katayama Index and modified Narumi-Katayama index for some families of dendrimers.
Eurasian Chemical Communications, Mar 11, 2020
Mathematical chemistry is the area of research engaged in new application of Mathematics in Chemi... more Mathematical chemistry is the area of research engaged in new application of Mathematics in Chemistry. Major areas of research in mathematical chemistry include chemical graph theory. Chemical graph theory applies graph theory to mathematical modeling of chemical phenomena. If G=(V(G),E(G)) is a connected graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, then the eccentric connectivity index of G (denoted by ξ(G)) was defined as ζ(G)=
Mathematical Biosciences and Engineering
The use of topological descriptors is the key method, regardless of great advances taking place i... more The use of topological descriptors is the key method, regardless of great advances taking place in the field of drug design. Descriptors portray the chemical characteristic of a molecule in numerical form, that is used for QSAR/QSPR models. The numerical values related with chemical constitutions that correlate the chemical structure with the physical properties refer to topological indices. The study of chemical structure with chemical reactivity or biological activity is termed quantitative structure activity relationship, in which topological index plays a significant role. Chemical graph theory is one such significant branch of science which plays a key role in QSAR/QSPR/QSTR studies. This work is focused on computing various degree-based topological indices and regression model of nine anti-malaria drugs. Regression models are fitted for computed indices values with 6 physicochemical properties of the anti-malaria drugs are studied. Based on the results obtained, an analysis is...
Journal of Discrete Mathematical Sciences and Cryptography
Abstract Irregularity indices are a special type of topological indices, first studied by Paul Er... more Abstract Irregularity indices are a special type of topological indices, first studied by Paul Erdös In this paper, we compute twelve degree-based irregularity topological indices for some networks like Butterfly networks, BF(r), Benes networks B(r), two important mesh derived networks namely MDN1, MDN2 with respect to the edge partition obtained for each such networks.
Journal of Discrete Mathematical Sciences and Cryptography
Abstract Topological indices are numerical parameters associated with underlying topology of a mo... more Abstract Topological indices are numerical parameters associated with underlying topology of a molecular structure. They are correlated with several physio-chemical properties of chemical compounds. Recently, Euclidean metric based topological index has been introduced named as Sombor index. Therefore, in this article, we will discuss combinatorial aspects and compute Sombor index, average Sombor index and the reduced Sombor index of line graph of silicate carbides Si 2 C 3 -I[p, q].
Journal of Information and Optimization Sciences, 2020
Mathematical topological characterization of chemical graphs gives information about some physica... more Mathematical topological characterization of chemical graphs gives information about some physical properties of molecules. Classical degree based topological indices of copper oxide have been recently calculated. Ve-degree and Ev-degree based topological indices have been newly defined in graph theory. In this study we investigate ve-degree topological properties of copper oxide. We calculate ve-degree Zagreb and Randić indices of copper oxide.
Journal of Discrete Mathematical Sciences and Cryptography, 2020
A topological index is a real number which is same under graph isomorphism and it is derived from... more A topological index is a real number which is same under graph isomorphism and it is derived from a graph by mathematically. In chemical graph theory, a molecular graph is a simple graph having no loops and multiple edges in which atoms and chemical bonds are represented by vertices and edges respectively. Topological indices defined on these chemical molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. In this paper, we compute general expressions
Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer... more Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as m:=move(G):=sup Γ {|Γ g ∖Γ|∣g∈G}. Let p be a prime, p≥5, and let move(G)=m. If G is a 2-group on each orbit, and p is the least odd prime dividing |G|, then n:=|Ω|≤p p-1(⌊2mp p-1⌋-1). Moreover, for an infinite family of groups the above bound is attained.
A regular graph G is said to be semisymmetric if its full automorphism group acts transitively on... more A regular graph G is said to be semisymmetric if its full automorphism group acts transitively on its edge-set but not on its vertex-set. It was shown by Folkman [5] that a regular edge-transitive graph of order 2 p or 2 p 2 is necessarily vertex-transitive, where p is a prime. In this paper, it is proved that there is no connected semisymmetric cubic graph of order 4 p 2, where p is a prime.