arXiv subjects

Nilanjan De

Publications and source records attributed to Nilanjan De.

17 recordsLinked to original sources

arXiv2019

QSPR analysis of some novel neighborhood degree based topological descriptors

Topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. In this work, some new indices based on neighbourhood degree sum of nodes are proposed. To make the computation of the novel indices convenient, an algorithm is designed. QSPR analysis of these newly introduced indices are studied here which reveals their predicting power. Some mathematical properties of these indices are also discussed here.

cs.DM↗

arXiv2019

On some new neighbourhood degree based indices

In this paper, four novel topological indices named as neighbourhood version of forgotten topological index (F_N), modified neighbourhood version of Forgotten topological index ($F_N^*$), neighbourhood version of second Zagreb index ($M_2^*$)and neighbourhood version of hyper Zagreb index ($HM_N$) are introduced. Here the relatively study depends on the structure-property regression analysis is made to test and compute the chemical applicability of these indices for the prediction of physicochemical properties of octane isomers. Also it is shown that these newly presented indices have well degeneracy property in comparison with other degree based topological indices. Some mathematical properties of these indices are also discussed here.

physics.chem-ph↗

arXiv2019

The general Zagreb index of lattice networks

A topological index is a real number which is derived from a network or a graph by mathematically that characterizes the whole of its structural properties. Recently, there are various topological indices that have been introduced in mathematical chemistry to predict the properties of molecular topology. Among, the degree based topological indices such as Zagreb indices, forgotten topological index, redefined Zagreb index, Randic index, general first Zagreb index, symmetric division deg index and hence so forth are most important, because of their chemical significance. In this work, we study the general Zagreb index of hexagonal and triangular lattice networks.

math.CO↗

arXiv2018

On Neighbourhood Zagreb index of product graphs

There is powerful relation between the chemical behaviour of chemical compounds and their molecular structures. Topological indices defined on these chemical molecular structures are capable to predict physical properties, chemical reactivity and biological activity. In this article, a new topological index named as Neighbourhood Zagreb index $(M_N)$ is presented. Here the chemical importance of this newly introduced index is studied and some explicit results for this index of different product graphs such as Cartesian, Tensor and Wreath product is derived. Some of these results are applied to obtain the Neighbourhood Zagreb index of several chemically important graphs and nano-structures.

math.CO↗

arXiv2017

Topological indices of k-th subdivision and semi total point graphs

Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and $H$. In this article, we present exact expressions for some topological indices of k-th subdivision graph and semi total point graphs respectively, which are a generalization of ordinary subdivision and semi total graph for $k\ge 1$.

math.CO↗

arXiv2017

F-index of graphs based on new operations related to the join of graphs

The forgotten topological index or F-index of a graph is defined as the sum of degree cube of all the vertices of the graph. This index was introduced by Gutman and Trinajestić more than 40 years ago. In this paper, we derive F-index of new operations of subdivision graphs related to the graphs join.

math.CO↗

arXiv2017

F-index of graphs based on four operations related to the lexicographic product

The forgotten topological index or F-index of a graph is defined as the sum of cubes of the degree of all the vertices of the graph. In this paper we study the F-index of four operations related to the lexicographic product on graphs which were introduced by Sarala et al. [D. Sarala, H. Deng, S.K. Ayyaswamya and S. Balachandrana, The Zagreb indices of graphs based on four new operations related to the lexicographic product, \textit{Applied Mathematics and Computation}, 309 (2017) 156--169.].

cs.DM↗

arXiv2017

Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs

The generalized hierarchical product of graphs was introduced by L. Barriére et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.

cs.DM↗

arXiv2017

Hyper Zagreb Index of Bridge and Chain Grpahs

Let G be a simple connected molecular graph with vertex set $V(G)$ and edge set $E(G)$. One important modification of classical Zagreb index, called hyper Zagreb index $HM(G)$ is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms $[{d_G}(u)+{d_G}(v)]^2$ over all the edges of $G$, where ${d_G}(u)$ denote the degree of the vertex $u$ of $G$. In this paper, the hyper Zagreb index of certain bridge and chain graphs are computed and hence using the derived results we compute the hyper Zagreb index of several classes of chemical graphs and nanostructures.

cs.DM↗

arXiv2017

On eccentricity version of Laplacian energy of a graph

The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and average degree of the vertices of G. Motivated by the work from Sharafdini et al. [R. Sharafdini, H. Panahbar, Vertex weighted Laplacian graph energy and other topological indices. J. Math. Nanosci. 2016, 6, 49-57.], in this paper we investigate the eccentricity version of Laplacian energy of a graph G.

cs.DM↗

arXiv2016

F-Index of Four Operations on Graphs

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph which was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced. In this paper we study the F-index of four operations on graphs which were introduced by Eliasi and Taeri [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, \textit{Discrete Appl. Math.}\textbf{157}(2009) 794--803.].

cs.DM↗

arXiv2016

F-index and coindex of some derived graphs

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

cs.DM↗

arXiv2016

Narumi-Katayama Index of Total Transformation Graphs

The Narumi-Katayama index of a graph was introduced in 1984 for representing the carbon skeleton of a saturated hydrocarbons and is defined as the product of degrees of all the vertices of the graph. In this paper, we examine the Narumi-Katayama index of different total transformation graphs.

cs.DM↗

arXiv2016

F-index of Total Transformation Graphs

The F-index of a graph $G$ is the sum of the cubes of the degrees of the vertices of $G$. In this paper, explicit expressions for the F-index of different transformation graphs of type ${{G}^{xyz}}$ with $x, y, z\in \{-, + \}$ are obtained. F-index for semitotal point graph and semitotal line graph are also obtained here.

cs.DM↗

arXiv2015

F-Index of Some Graph Operations

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total $π$-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53(4)(2015) 1184--1190.] reinvestigated the index and named it "forgotten topological index" or "F-index". In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nano-structures.

math.CO↗

arXiv2014

Connective eccentric index of some graph operations

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction and splice of graphs.

math.CO↗

arXiv2014

Bounds for the modified eccentric connectivity index

The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph. This is a generalization of eccentric connectivity index. In this paper, we derive some upper and lower bounds for the modified eccentric connectivity index in terms of some graph parameters such as number of vertices, number of edges, radius, minimum degree, maximum degree, total eccentricity, the first and second Zagreb indices, Weiner index etc.

math.CO↗