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
Recommended Citation
Fiedler, M., & Nikiforov, V. (2010). Spectral radius and Hamiltonicity of graphs. Linear Algebra and Its Applications, 432 (9), 2170-2173. https://doi.org/10.1016/j.laa.2009.01.005
