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Revisiting two classical results on graph spectra

Vladimir Nikiforov
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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).

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Vladimir Nikiforov. 2006-09-04. Revisiting two classical results on graph spectra. https://arxiv.org/abs/math/0609111

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