Abstract
Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues lambda(1), lambda(2), ... , lambda(n). The energy E(G) of the graph G is defined as E(G) = Sigma(n)(i=1) vertical bar lambda(i)vertical bar In this paper, we obtain the upper bounds for the energy E(G) in terms of the vertex covering number tau, the clique number omega, the number of edges m, maximum vertex degree d(1) and second maximum vertex degree d(2) of the connected graph G. These upper bounds improve some of the recently known upper bounds.