Abstract
ABSTRACTThe 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.
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