Walks and the spectral radius of graphs
Abstract
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique number, and wk(G) for the number of its k-walks. We prove that the inequalitiesfrac(wq + r (G), wq (G)) ≤ μr (G) ≤ frac(ω (G) - 1, ω (G)) wr (G)hold for all r > 0 and odd q > 0. We also generalize a number of other bounds on μ(G) and characterize semiregular and pseudo-regular graphs in spectral terms. © 2006 Elsevier Inc. All rights reserved.
Publication Title
Linear Algebra and Its Applications
Recommended Citation
Nikiforov, V. (2006). Walks and the spectral radius of graphs. Linear Algebra and Its Applications, 418 (1), 257-268. https://doi.org/10.1016/j.laa.2006.02.003
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