Hosoya Index of L-Type Polyphenyl Spiders

Abstract

The polyphenyl system is composed of n hexagons obtained from two adjacent hexagons that are sticked by a path with two vertices. The Hosoya index of a graph G is defined as the total number of the independent edge sets of G. In this paper, we give a computing formula of Hosoya index of a type of polyphenyl system. Furthermore, we characterize the extremal Hosoya index of the type of polyphenyl system.