Title

Bounds on graph eigenvalues II

Abstract

We prove three results about the spectral radius μ(G) of a graph G:(a)Let Tr (n) be the r-partite Turán graph of order n. If G is a Kr + 1-free graph of order n, thenμ (G) < μ (Tr (n))unless G = Tr (n).(b)For most irregular graphs G of order n and size m,μ (G) - 2 m / n > 1 / (2 m + 2 n) .(c)Let 0 ≤ k ≤ l. If G is a graph of order n with no K2 + over(K, -)k + 1 and no K2, l + 1, thenμ (G) ≤ min G), (k - l + 1 + sqrt((k - l + 1)2 + 4 l (n - 1))) / 2} . © 2007 Elsevier Inc. All rights reserved.

Publication Title

Linear Algebra and Its Applications

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