Two Classes of Topological Indices of Phenylene Molecule Graphs

摘要

A phenylene is a conjugated hydrocarbons molecule composed of six- and four-membered rings. The matching energy of a graph G is equal to the sum of the absolute values of the zeros of the matching polynomial of G, while the Hosoya index is defined as the total number of the independent edge sets of G. In this paper, we determine the extremal graph with respect to the matching energy and Hosoya index for all phenylene chains.