Hosoya Index of Two Types of Four Leaves Polyphenyl Systems^*

ABSTRACT

The polyphenyl system is composed of n hexagons, where consecutive hexagons 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 two computation formulas of Hosoya index of two types of four leaves polyphenyl systems. In particular, we characterize the extremal Hosoya index of two types of four leaves polyphenyl systems.

Keywords:

• Four leaves polyphenyl system
• Hosoya index
• polyphenyl chain

Additional information

Funding

This work is supported by NSFC (11761056), NSF of Qinghai (2016-ZJ-947Q), Education department of Shaanxi province(15JK1135, 2016JK1141) and Shaanxi university of technology (SLGQD14-14, SLGKY15-37).