Topological Invariants of Generalized Splitting Graphs and k-Shadow Graphs

Abstract

A topological index or an invariant can be defined as a function from a set of graphs to the real line. Topological indices are invariant under graph isomorphism. This paper deals with the general expressions for various topological indices of two derived graphs called generalized splitting graphs and k-shadow graphs. In particular this manuscript discuss about the first Zagreb index, second Zagreb index, F-index, hyper-Zagreb index, symmetric division degree index, first and the second multiplicative Zagreb indices and a lower bound for the irregularity index of generalized splitting graphs and k-shadow graphs.

Key words and phrases. Topological invariants, splitting graph, k-shadow graph.

2000 Mathematics Subject Classification. 05C92