Revisiting two classical results on graph spectra

Details Revisiting two classical results on graph spectra Revisiting two classical results on graph spectra

2006-09-04

arxiv.org/abs/math/0609111v1

Mathematics

Combinatorics

Scientific paper

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).

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