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 λ1, λ2, …, λn. The energy E(G) of the graph G is defined as E(G) = ∑i = 1n∣λi∣. 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 d1 and second maximum vertex degree d2 of the connected graph G. These upper bounds improve some of the recently known upper bounds.

Keywords

• graph energy, vertex covering number, clique number, maximum degree