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

Hilal A. Ganie (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)
U. Samee (Department of Mathematics, Islamia College for Science and Commerce, Srinagar, Kashmir, India)
S. Pirzada (Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India)
Ahmad M. Alghamadi (Department of Mathematical Sciences, Umm Alqura University, Makkah, Saudi Arabia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications

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.