Revisiting two classical results on graph spectra

2006/09/04 by Vladimir Nikiforov, Nikiforov, Vladimir
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Graph Theory and Algorithms #Graph theory and applications #math.AC #math.CO #msc:05C50

paper · pdf · doi:10.48550/arxiv.math/0609111

arxiv created 2006/09/04 · openalex publication_date 2006/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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