Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 430, Issue 11-12, Pages 2898-2905Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2009.01.002
Keywords
4-Cycles; Graph spectral radius; Graphs with no 4-cycles; Friendship graph
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Suppose that G is a graph with n vertices and m edges, and let mu be the spectral radius of its adjacency matrix., n Recently we showed that if G has no 4-cycle, then mu(2) - mu <= n - 1, with equality if and only if G is the friendship graph. Here we prove that if m >= 9 and G has no 4-cycle, then mu(2) <= M, with equality if G is a star. For 4 <= m <= 8 this assertion fails. (C) 2009 Elsevier Inc. All rights reserved.
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