Computation of Gutman index of some cactus chains

Abstract

Let G be a finite connected graph of order n. The Gutman index Gut(G) of G is defined as ∑_{{x, y} ⊆ V(G)}deg(x)deg(y)d(x, y), where deg(x) is the degree of vertex x ∈ G and d(x, y) is the distance between vertices x and y in G. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this paper we compute the exact value of Gutman index of some cactus chains.