Revisiting two classical results on graph spectra
Combinatorics
2007-05-23 v1 Commutative Algebra
Abstract
Let mu(G) and mu_min(G) be the largest and smallest eigenvalues of the adjacency matricx of a graph G. We refine quantitatively the following two results on graph spectra. (i) if H is a proper subgraph of a connected graph G, then mu(G)>mu(H). (ii) if G is a connected nonbipartite graph, then mu(G)>-mu_min(G).
Cite
@article{arxiv.math/0609111,
title = {Revisiting two classical results on graph spectra},
author = {Vladimir Nikiforov},
journal= {arXiv preprint arXiv:math/0609111},
year = {2007}
}