Maxima of the Q-index: forbidden even cycles
نویسندگان
چکیده
Let G be a graph of order n and let q (G) be the largest eigenvalue of the signless Laplacian of G. Let Sn,k be the graph obtained by joining each vertex of a complete graph of order k to each vertex of an independent set of order n − k; and let S n,k be the graph obtained by adding an edge to Sn,k. It is shown that if k ≥ 2, n ≥ 400k2, and G is a graph of order n, with no cycle of length 2k + 2, then q (G) < q ( S n,k ) , unless G = S n,k. This result completes the proof of a conjecture of de Freitas, Nikiforov and Patuzzi. AMS classification: 15A42, 05C50
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تاریخ انتشار 2015