The matching energy of graphs with given edge connectivity

Abstract

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 maximum matching energy among all connected graph with order $n$ and edge connectivity $k$.