Some Inequalities for the Largest Eigenvalue of a Graph

Authors:
V. Nikiforov
Affiliations:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, TN 38152, USA (e-mail: vlado-nikiforov@hotmail.com)
Venue:
Combinatorics, Probability and Computing
Year:
2002

Citing 6
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Abstract

Let λ(G) be the largest eigenvalue of the adjacency matrix of a graph G: We show that if G is Kp+1-free then ***** insert CODING here *****This inequality was first conjectured by Edwards and Elphick in 1983 and supersedes a series of previous results on upper bounds of λ(G).Let Ti denote the number of all i-cliques of G, λ = λ(G) and p = cl(G): We show ***** insert equation here *****Let δ be the minimal degree of G. We show ***** insert equation here *****This inequality supersedes inequalities of Stanley and Hong. It is sharp for regular graphs and for a class of graphs which are in some sense maximally irregular.