Abstract
The matching energy of a graph G is ME(G)=2π∫0∞1x2ln[∑k≥0m(G,k)x2k]dx, and the Hosoya index of G is Z(G)=∑k≥0m(G,k), where m(G,k) is the number of k-matchings in G. In this note, we first determine the maximum values of m(G,k) in all connected bipartite graphs with n vertices and a given connectivity. And then we determine the maximum matching energy (resp. Hosoya index) among all connected bipartite graphs with n vertices and a given (edge) connectivity and characterize the corresponding extremal graphs.
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