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Linear combinations of graph eigenvalues

Vladimir Nikiforov
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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 max{F(G):v(G)=n} generalizes a number of problems raised previously in the literature. We show that the limit max{F(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.

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Vladimir Nikiforov. 2006-10-02. Linear combinations of graph eigenvalues. https://arxiv.org/abs/math/0608198

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