2010
DOI: 10.1016/j.laa.2009.08.029
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Eigenvalues and edge-connectivity of regular graphs

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Cited by 54 publications
(47 citation statements)
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“…Finally we note a recent result of Cioabǎ [4] relevant to our consideration of regular star complements. …”
Section: Proofmentioning
confidence: 74%
See 1 more Smart Citation
“…Finally we note a recent result of Cioabǎ [4] relevant to our consideration of regular star complements. …”
Section: Proofmentioning
confidence: 74%
“…Since V (H) is an (s, 1)-regular set in G * , we have µ = s − 1 by Lemma 2.6. Assertion (i), due to Cioabǎ [4], holds whether or not µ is a main eigenvalue. Indeed, if H has order t ≤ 2s + 1 then κ (H) = s ≥ k by Lemma 2.7, while if t ≥ 2s + 2 then ν 2 ≤ s − …”
Section: Proofmentioning
confidence: 99%
“…Cioabǎ [3] presented examples for sharpness in the upper bound on λ 2 (G) for a d-regular simple graph G to guarantee that G is either 2-edge-connected or 3-edge-connected. In this section, we present a smallest d-regular multigraph H d,1 with κ (H d,1 ) = 1 and with…”
Section: The Constructionmentioning
confidence: 99%
“…This result is best possible in a sense that there exists a d-regular simple graph H with λ 2 (H) = π(d) and with κ (H) = 1 (See [3]). …”
Section: Introductionmentioning
confidence: 99%
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