Nilanjan De

The F-coindex of some graph operations

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjunction, symmetric difference of graphs and hence apply our results to find the F-coindex of different chemically interesting molecular graphs and nano-structures.

Modified Eccentric Connectivity of Generalized Thorn Graphs

The thorn graph of a given graph is obtained by attaching pendent vertices to each vertex of . The pendent edges, called thorns of , can be treated as or , so that a thorn graph is generalized by replacing by and by and the respective generalizations are denoted by and . 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 in a hydrogen suppressed molecular structure. In this paper, we give the modified eccentric connectivity index and the concerned polynomial for the thorn graph and the generalized thorn graphs and .

On Some Bounds and Exact Formulae for Connective Eccentric Indices of Graphs under 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.

The Forgotten Topological Index of Graphs Based on New Operations Related to the Join of Graphs

The sum of degree cube of all the vertices of a graph is known as the F-index or the “forgotten topological index” of that graph. In the present work, we study the “forgotten topological index” of new operations of different subdivision-related graphs based on the join of graphs.

The (a,b)-Zagreb index of some derived networks

ABSTRACT There is a very wide application of mathematics in communication theory, signal processing and networking. A network is formed by nodes communicating with each other. Graph theory plays a vital role in the area of networking research. A topological index is a numeric quantity obtained from a graph structure which is invariant under graph isomorphism. In this study, we obtained a generalized degree-based topological index, called -Zagreb index of some derived networks such as Sierpinski network, butterfly network, Benes network and mesh-derived network and hence consider some particular cases.

The Generalized Zagreb Index of Some Carbon Structures

Abstract In chemical graph theory, chemical structures are model edthrough a graph where atoms are considered as vertices and edges are bonds between them. In chemical sciences, topological indices are used for understanding the physicochemical properties of molecules. In this work, we study the generalized Zagreb index for three types of carbon allotrope’s theoretically.