Abstract
The matching energy of a graph G is defined as the sum of the absolute values of thezeros of the matching polynomial of G. The Hosoya index of a graph G is defined as the total number of matchingsof G. In this paper, the matching energy and Hosoya index of the a special class of tricyclic graphs G(m 1, m 2, m 3) were investigated, and orderings of tricyclic graphs G(m 1, m 2, m 3) with respect to matching energy and Hosoya index are obtained.
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