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

Electronic Journal of Graph Theory and Applications

Ahmad M. Alghamadi¹  U. Samee²  S. Pirzada³  Hilal A. Ganie³ 

[1] Department of Mathematical Sciences, Umm Alqura University, Makkah, Saudi Arabia;Department of Mathematics, Islamia College for Science and Commerce, Srinagar, Kashmir, India;Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India;

关键词: graph energy, vertex covering number, clique number, maximum degree;   

DOI  :  10.5614/ejgta.2019.7.2.9

来源: DOAJ

【 摘 要 】

Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues λ₁, λ₂, …, λ_n. The energy E(G) of the graph G is defined as E(G) = ∑_i = 1ⁿ∣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 d₁ and second maximum vertex degree d₂ of the connected graph G. These upper bounds improve some of the recently known upper bounds.

【 授权许可】

Unknown