Degree based topological invariants of splitting graph

Abstract

Topological invariants are the graph theoretical tools to the theoretical chemists, that correlates the molecular structure with several chemical reactivity, physical properties or biological activity numerically. A function having a set of networks(graph, molecular structure) as its domain and a set of real numbers as its range is referred as a topological invariant(index). Topological invariants are numerical quantity of a network that are invariant under graph isomorphism. Topological invariants such as Zagreb index, Randić index and multiplicative Zagreb indices are used to predict the bioactiviy of chemical compounds in QSAR/QSPR study. In this paper, we compute the general expression of certain degree based topological invariants such as second Zagreb index, F-index, Hyper-Zagreb index, Symmetric division degree index, irregularity of Splitting graph. And also we obtain upper bound for first and second multiplicative Zagreb indices of Splitting graph of a graph H, (S′(H)).