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Abstract: Let G be a graph with n vertices and muG be the largest eigenvalue of theadjacency matrix of G. We study how large muG can be when G does not containcycles and paths of specified order. In particular, we determine the maximumspectral radius of graphs without paths of given length, and give tight boundson the spectral radius of graphs without given even cycles. We also raise anumber of natural open problems.



Author: Vladimir Nikiforov

Source: https://arxiv.org/



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