The maximum spectral radius of C4-free graphs of given order and size


Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix. Recently we showed that if G has no 4-cycle, then μ2 - μ ≤ 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 μ2 ≤ m, with equality if G is a star. For 4 ≤ m ≤ 8 this assertion fails. © 2009 Elsevier Inc. All rights reserved.

Publication Title

Linear Algebra and Its Applications