Hosoya polynomial of some cactus chains

Abstract

Let $ G=(V,E) $ be a simple graph. Hosoya polynomial of G is $ H(G,x)=\\sum _{\\{u,v\\}\\subseteq V(G)} x^{d(u,v)} $, where d(u, v) denotes the distance between vertices u and v. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this paper we compute the Hosoya polynomial of some cactus chains. As a consequence, Wiener and hyper-Wiener indices of these kind of chains are also obtained.