The matching energy of graphs with given edge connectivity

Let G be a simple graph of order n and \(\mu_{1},\mu_{2},\ldots,\mu_{n}\) the roots of its matching polynomial. The matching energy of G is defined as the sum \(\sum_{i=1}^{n}|\mu_{i}|\). Let \(K_{n-1,1}^{k}\) be the graph obtained from \(K_{1}\cup K_{n-1}\) by adding k edges between \(V(K_{1})\) and \(V(K_{n-1})\). In this paper, we show that \(K_{n-1,1}^{k}\) has the maximum matching energy among the connected graphs with order n and edge connectivity k.