The matching energy of graphs with given parameters

Abstract

Gutman and Wagner [I. Gutman, S. Wagner, The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177–2187] defined the matching energy of a graph and gave some properties and asymptotic results of the matching energy. In this paper, we characterize the connected graph $G$ with the connectivity $\kappa$ (resp. chromatic number $\chi$) which has the maximum matching energy.