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An asymptotically tight bound on the Q-index of graphs with forbidden cycles by Nikiforov, V. is a scholarly article available to read on EtoBox.

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Let G be a graph of order n and let q(G) be that largest eigenvalue of the signless Laplacian of G. In this note it is shown that if k>1 and q(G)>=n+2k-2, then G contains cycles of length l whenever 2<l<2k+3. This bound is asymptotically tight. It implies an asymptotic solution to a recent conjecture about the maximum q(G) of a graph G with no cycle of a specified length.

Author

Nikiforov, V.

Published

2013

Language

EN