Walks and the spectral radius of graphs

Vladimir Nikiforov
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
Given a graph G, write µ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique number, and w k (G) for the number of its k-walks. We prove that the inequalities 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.
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