Linear combinations of graph eigenvalues
Combinatorics
2007-05-23 v2 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.math/0608198,
title = {Linear combinations of graph eigenvalues},
author = {Vladimir Nikiforov},
journal= {arXiv preprint arXiv:math/0608198},
year = {2007}
}
Comments
Some calculation errors from the first version have been corrected