On the Hosoya Index and the Merrifield-Simmons Index of Bicyclic Graphs with Given Matching Number

Abstract

Let \(\mathcal{B}(n, a)\) be the set of bicyclic graphs on \(n\) vertices with matching number \(\alpha\). In this paper, we characterize the extremal bicyclic graph with minimal Hosoya index and maximal Merrifield-Simmons index in \(\mathcal{B}(n, a)\).