Computation of Gutman index of some cactus chains

Abstract

Let G be a finite connected graph of order n . The Gutman index G u t ( G ) of G is defined as ∑ { x , y } ⊆ V ( G ) d e g ( x ) d e g ( y ) d ( x , y ) , where d e g ( 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.