Computing F-Index of Different Corona Products of Graphs

Abstract

F-index of a graph is equal to the sum of cubes of degree of all the vertices of a given graph. Among different products of graphs, as corona product of two graphs is one of most important, in this study, the explicit expressions for F-index of different types of corona product of are obtained. Introduction A topological index is defined as a real valued function, which maps each molecular graph to a real number and is necessarily invariant under automorphism of graphs. There are various topological indices having strong correlation with the physicochemical characteristics and have been found to be useful in isomer discrimination, quantitative structure-activity relationship (QSAR) and structure-property relationship (QSPR). In this article, as a molecular graph, we consider only finite, connected and undirected graphs without any self-loops or multiple edges. Let G be such a graph with vertex set V (G) and edge set E(G) so that the order and size of G is equal to n and m respectively. Let the edge connecting the vertices u and v is denoted by uv. Let, the degree of the vertex v in G is denoted by dG(v), which is the number of edges incident to v, that is, the number of first neighbors of v. Among various degree-based topological indices, the first (M1(G)) and the second (M2(G)) Zagreb index of a G are one of the oldest and most studied topological indices introduced in [13] by Gutman and Trinajstić and defined as