TY - JOUR
T1 - Sharp spectral bounds for the edge-connectivity of regular graphs
AU - Suil, O.
AU - Park, Jeong Rye
AU - Park, Jongyook
AU - Zhang, Wenqian
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/5
Y1 - 2023/5
N2 - Let λ2(G) and κ′(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, Cioabǎ gave sharp upper bounds for λ2(G) in an r-regular simple graph G to guarantee that κ′(G)≥t+1. In this paper, we resolve this question for all t≥3; if G is an r-regular simple graph with [Formula presented], then κ′(G)≥t+1, and for odd t, if G is an r-regular simple graph with [Formula presented], then κ′(G)≥t+1.
AB - Let λ2(G) and κ′(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, Cioabǎ gave sharp upper bounds for λ2(G) in an r-regular simple graph G to guarantee that κ′(G)≥t+1. In this paper, we resolve this question for all t≥3; if G is an r-regular simple graph with [Formula presented], then κ′(G)≥t+1, and for odd t, if G is an r-regular simple graph with [Formula presented], then κ′(G)≥t+1.
UR - http://www.scopus.com/inward/record.url?scp=85150457722&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2023.103713
DO - 10.1016/j.ejc.2023.103713
M3 - Article
AN - SCOPUS:85150457722
SN - 0195-6698
VL - 110
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103713
ER -