Some upper bounds for the energy of graphs

摘要

Let G = (V,E) be a graph with n vertices and e edges. Denote V(G) = {v 1,v 2,...,v n }. The 2-degree of v i , denoted by t i , is the sum of degrees of the vertices adjacent to $v_i, 1leqslant ileqslant n$ . Let σ i be the sum of the 2-degree of vertices adjacent to v i . In this paper, we present two sharp upper bounds for the energy of G in terms of n, e, t i , and σ i , from which we can get some known results. Also we give a sharp bound for the energy of a forest, from which we can improve some known results for trees.