On the Detour Based Indices

Abstract

Topological index is a real value associated with a graph that should be structurally invariant. Many topological indices were defined, and many among them have been used to model chemical and pharmacological properties, as well as many other features of molecules. We study two topological indices based on detour distance. Detour index for any graph that is connected is defined as maximum distances or detour distances between every unordered paired vertices of . Detour Harary index for any graph that is connected is defined as the sum of reciprocal of the maximum distances or detour distances between every unordered paired vertices of . Here, in this paper we establish formulae to calculate the Detour index and detour Harary index of a few graph structures and also corona product of two particular graphs. Also we compare the results for both these indices .