Two Classes of Topological Indices of Phenylene Molecule Graphs

Abstract EN

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.