Upper bounds on the energy of graphs in terms of matching number

The energy of a graph G, ?(G), is the sum absolute values eigenvalues its adjacency matrix. matching number ?(G) edges in maximum matching. In this paper, for connected G order n with largest vertex degree ? 6 we present two new upper bounds graph: (n-1)?? and 2?(G)??. latter one improves recently obtained bound {2?(G)?2?e + 1, if ?e even; ?(G)(? 2?a ?a-2?a), otherwise, where stands edge = 2(?e 1). We also short proof result several open problems.