Sharp spectral bounds for the edge-connectivity of regular graphs

초록

Let ),2(G) and K '(G) be the second largest eigenvalue and the edge-connectivity of a graph G, respectively. Let r be a positive integer at least 3. For t = 1 or 2, Cioaba gave sharp upper bounds for ),2(G) in an r-regular simple graph G to guarantee that K '(G) > t+1. In this paper, we resolve this question for all t > 3; if G is an r-regular simple graph with ),2(G) < r-3+4(r+3)2-8t , 2 graph with ),2(G) < r-4+4(r+4)2-8t then K '(G) > t + 1, and for odd t, if G is an r-regular simple , then K '(G) > t + 1. 2 (c) 2023 Elsevier Ltd. All rights reserved.

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