Bounds for graph energy in terms of vertex covering and clique numbers

Abstract

Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues λ 1 , λ 2 , … , λ n . The energy E( G ) of the graph G is defined as E( G ) = ∑ i = 1 n ∣ λ i ∣ . In this paper, we obtain the upper bounds for the energy E( G ) in terms of the vertex covering number τ , the clique number ω , 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.