Linear combinations of graph eigenvalues

2006/08/08 by Nikiforov, Vladimir · 1 citation
#05C50 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608198

Abstract

Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding maxF(G):v(G)=n generalizes a number of problems raised previously in the literature. We show that the limit maxF(G):v(G)=n/n exists when n tends to infinity. We also answer a question of Gernert about the sum of the two maximal eigenvalues of a graph.

Cited by

• The Exact Maximum of the Spectral Sum of Graphs

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