Title

Spectral radius and Hamiltonicity of graphs

Abstract

Let G be a graph of order n and μ (G) be the largest eigenvalue of its adjacency matrix. Let over(G, -) be the complement of G. Write Kn - 1 + v for the complete graph on n - 1 vertices together with an isolated vertex, and Kn - 1 + e for the complete graph on n - 1 vertices with a pendent edge. We show that:. If μ (G) ≥ n - 2, then G contains a Hamiltonian path unless G = Kn - 1 + v; if strict inequality holds, then G contains a Hamiltonian cycle unless G = Kn - 1 + e. If μ (over(G, -)) ≤ sqrt(n - 1), then G contains a Hamiltonian path unless G = Kn - 1 + v. If μ (over(G, -)) ≤ sqrt(n - 2), then G contains a Hamiltonian cycle unless G = Kn - 1 + e. © 2009 Elsevier Inc. All rights reserved.

Publication Title

Linear Algebra and Its Applications

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