The spectral radius of graphs without paths and cycles of specified length

Details The spectral radius of graphs without paths and cycles of specified length The spectral radius of graphs without paths and cycles of specified length

2009-03-31

arxiv.org/abs/0903.5351v1

Mathematics

Combinatorics

Scientific paper

Let G be a graph with n vertices and mu(G) be the largest eigenvalue of the adjacency matrix of G. We study how large mu(G) can be when G does not contain cycles and paths of specified order. In particular, we determine the maximum spectral radius of graphs without paths of given length, and give tight bounds on the spectral radius of graphs without given even cycles. We also raise a number of natural open problems.

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