Computation of Gutman index of some cactus chains

Ali Sadeghieh (Department of Mathematics, Islamic Azad University Yazd branch, Yazd, Iran)
Nima Ghanbari (Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.)
Saeid Alikhani (Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications

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.