DURBAR MAJI - Academia.edu (original) (raw)

Papers by DURBAR MAJI

Research paper thumbnail of The Reformulated F-Index of Vertex and Edge F-Join of Graphs

Journal of Chemistry

The valency based topological indices (TIs) are defined by algebraic functions as the chemical gr... more The valency based topological indices (TIs) are defined by algebraic functions as the chemical graph theory tools in which the structural parameters are used as input and the output is related with the topology of chemical species. In theoretical chemistry, the TIs are mainly used to investigate/develop the QSAR and QSPR investigations of the molecular graphs. The Reformulated F-index or RFI is one such kind of TIs. The RFI for a molecular graph Y is defined as R F Y = ∑ u v ∈ E Y d Y u + d Y v − 2 3 , where d Y u is the degree of a vertex u in Y . In this paper, we study the RFI for vertex and edge version of F-join of given general graphs which are related to subdivision and total graph.

Research paper thumbnail of The first entire Zagreb index of various corona products and their bounds

Journal of Mathematical and Computational Science, 2021

The First Entire Zagreb Index (FEZI) of a (molecular) graph was introduced by Alwardi et al. [2] ... more The First Entire Zagreb Index (FEZI) of a (molecular) graph was introduced by Alwardi et al. [2] as the sum of the squares of degree of all the vertices and edges of the given graph. In this paper, the exact expressions for the FEZI of two graphs of several types of Corona products are established. Finally, the obtained results are applied to compute the bounds for the FEZI of two graphs.

Research paper thumbnail of On the Reformulated Second Zagreb Index of Graph Operations

Journal of Chemistry, 2021

Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the... more Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the graphs in QSAR/QSPR investigation. The reformulated second Zagreb index (RSZI) is such a novel TI having good correlations with various physical attributes, chemical reactivities, or biological activities/properties. The RSZI is defined as the sum of products of edge degrees of the adjacent edges, where the edge degree of an edge is taken to be the sum of vertex degrees of two end vertices of that edge with minus 2. In this study, the behaviour of RSZI under graph operations containing Cartesian product, join, composition, and corona product of two graphs has been established. We have also applied these results to compute RSZI for some important classes of molecular graphs and nanostructures.

Research paper thumbnail of Some New Upper Bounds for the Y -Index of Graphs

Journal of Mathematics, 2022

In mathematical chemistry, the topological indices with highly correlation factor play a leading ... more In mathematical chemistry, the topological indices with highly correlation factor play a leading role specifically for developing crucial information in QSPR/QSAR analysis. Recently, there exists a new graph invariant, namely, Y -index of graph proposed by Alameri as the sum of the fourth power of each and every vertex degree of that graph. The approximate range of the descriptors is determined by obtaining the bounds for the topological indices of graphs. In this paper, firstly, some upper bounds for the Y -index on trees with several types of domination number are studied. Secondly, some new bounds are also presented for this index of graphs in terms of relevant parameters with other topological indices. Additionally, a new idea on bounds for the Y -index by applying binary graph operations is computed.

Research paper thumbnail of On the Inverse Problem for Some Topological Indices

Journal of Mathematics

The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numer... more The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numerical relations to TIs. Mathematically, the IP can be expressed as follows: given a graph parameter/TI that assigns a non-negative integer value g to every graph within a given family G of graphs, find some G ∈ G for which TI G = g . It was initiated by the Zefirov group in Moscow and later Gutman et al. proposed it. In this paper, we have established the IP only for the Y -index, Gourava indices, second hyper-Zagreb index, reformulated first Zagreb index, and reformulated F -index since they are closely related to each other. We have also studied the same which is true for the molecular, tree, unicyclic, and bicyclic graphs.

Research paper thumbnail of Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs

In chemical graph theory, forgotten topological index or F-index plays a crucial role to collect ... more In chemical graph theory, forgotten topological index or F-index plays a crucial role to collect information about the properties of chemical compounds. The kth generalized transformation graphs of a molecular graph preserve the entire information on the molecular topology contained in the relevant molecular graph. In this paper, some exact expressions of the F-index and its co-index for the kth generalized transformation graphs are obtained. Also, the Zagreb polynomials, Zagreb co-polynomials and their complements are computed.

Research paper thumbnail of A Novel Graph Invariant: The Third Leap Zagreb Index Under Several Graph Operations

Discrete Mathematics, Algorithms and Applications

The third leap Zagreb index of a graph [Formula: see text] is denoted as [Formula: see text] and ... more The third leap Zagreb index of a graph [Formula: see text] is denoted as [Formula: see text] and is defined as [Formula: see text], where [Formula: see text] and [Formula: see text] are the 2-distance degree and the degree of the vertex [Formula: see text] in [Formula: see text], respectively. The first, second and third leap Zagreb indices were introduced by Naji et al. [A. M. Naji, N. D. Soner and I. Gutman, On leap Zagreb indices of graphs, Commun. Combin. Optim. 2(2) (2017) 99–117] in 2017. In this paper, the behavior of the third leap Zagreb index under several graph operations like the Cartesian product, Corona product, neighborhood Corona product, lexicographic product, strong product, tensor product, symmetric difference and disjunction of two graphs is studied.

Research paper thumbnail of The Reformulated F-Index of Vertex and Edge F-Join of Graphs

Journal of Chemistry

The valency based topological indices (TIs) are defined by algebraic functions as the chemical gr... more The valency based topological indices (TIs) are defined by algebraic functions as the chemical graph theory tools in which the structural parameters are used as input and the output is related with the topology of chemical species. In theoretical chemistry, the TIs are mainly used to investigate/develop the QSAR and QSPR investigations of the molecular graphs. The Reformulated F-index or RFI is one such kind of TIs. The RFI for a molecular graph Y is defined as R F Y = ∑ u v ∈ E Y d Y u + d Y v − 2 3 , where d Y u is the degree of a vertex u in Y . In this paper, we study the RFI for vertex and edge version of F-join of given general graphs which are related to subdivision and total graph.

Research paper thumbnail of The first entire Zagreb index of various corona products and their bounds

Journal of Mathematical and Computational Science, 2021

The First Entire Zagreb Index (FEZI) of a (molecular) graph was introduced by Alwardi et al. [2] ... more The First Entire Zagreb Index (FEZI) of a (molecular) graph was introduced by Alwardi et al. [2] as the sum of the squares of degree of all the vertices and edges of the given graph. In this paper, the exact expressions for the FEZI of two graphs of several types of Corona products are established. Finally, the obtained results are applied to compute the bounds for the FEZI of two graphs.

Research paper thumbnail of On the Reformulated Second Zagreb Index of Graph Operations

Journal of Chemistry, 2021

Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the... more Topological indices (TIs) are expressed by constant real numbers that reveal the structure of the graphs in QSAR/QSPR investigation. The reformulated second Zagreb index (RSZI) is such a novel TI having good correlations with various physical attributes, chemical reactivities, or biological activities/properties. The RSZI is defined as the sum of products of edge degrees of the adjacent edges, where the edge degree of an edge is taken to be the sum of vertex degrees of two end vertices of that edge with minus 2. In this study, the behaviour of RSZI under graph operations containing Cartesian product, join, composition, and corona product of two graphs has been established. We have also applied these results to compute RSZI for some important classes of molecular graphs and nanostructures.

Research paper thumbnail of Some New Upper Bounds for the Y -Index of Graphs

Journal of Mathematics, 2022

In mathematical chemistry, the topological indices with highly correlation factor play a leading ... more In mathematical chemistry, the topological indices with highly correlation factor play a leading role specifically for developing crucial information in QSPR/QSAR analysis. Recently, there exists a new graph invariant, namely, Y -index of graph proposed by Alameri as the sum of the fourth power of each and every vertex degree of that graph. The approximate range of the descriptors is determined by obtaining the bounds for the topological indices of graphs. In this paper, firstly, some upper bounds for the Y -index on trees with several types of domination number are studied. Secondly, some new bounds are also presented for this index of graphs in terms of relevant parameters with other topological indices. Additionally, a new idea on bounds for the Y -index by applying binary graph operations is computed.

Research paper thumbnail of On the Inverse Problem for Some Topological Indices

Journal of Mathematics

The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numer... more The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numerical relations to TIs. Mathematically, the IP can be expressed as follows: given a graph parameter/TI that assigns a non-negative integer value g to every graph within a given family G of graphs, find some G ∈ G for which TI G = g . It was initiated by the Zefirov group in Moscow and later Gutman et al. proposed it. In this paper, we have established the IP only for the Y -index, Gourava indices, second hyper-Zagreb index, reformulated first Zagreb index, and reformulated F -index since they are closely related to each other. We have also studied the same which is true for the molecular, tree, unicyclic, and bicyclic graphs.

Research paper thumbnail of Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs

In chemical graph theory, forgotten topological index or F-index plays a crucial role to collect ... more In chemical graph theory, forgotten topological index or F-index plays a crucial role to collect information about the properties of chemical compounds. The kth generalized transformation graphs of a molecular graph preserve the entire information on the molecular topology contained in the relevant molecular graph. In this paper, some exact expressions of the F-index and its co-index for the kth generalized transformation graphs are obtained. Also, the Zagreb polynomials, Zagreb co-polynomials and their complements are computed.

Research paper thumbnail of A Novel Graph Invariant: The Third Leap Zagreb Index Under Several Graph Operations

Discrete Mathematics, Algorithms and Applications

The third leap Zagreb index of a graph [Formula: see text] is denoted as [Formula: see text] and ... more The third leap Zagreb index of a graph [Formula: see text] is denoted as [Formula: see text] and is defined as [Formula: see text], where [Formula: see text] and [Formula: see text] are the 2-distance degree and the degree of the vertex [Formula: see text] in [Formula: see text], respectively. The first, second and third leap Zagreb indices were introduced by Naji et al. [A. M. Naji, N. D. Soner and I. Gutman, On leap Zagreb indices of graphs, Commun. Combin. Optim. 2(2) (2017) 99–117] in 2017. In this paper, the behavior of the third leap Zagreb index under several graph operations like the Cartesian product, Corona product, neighborhood Corona product, lexicographic product, strong product, tensor product, symmetric difference and disjunction of two graphs is studied.