Linear combinations of graph eigenvalues
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.
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