Edge-connectivity in regular multigraphs from eigenvalues

Suil, O

doi:10.1016/j.laa.2014.09.015

Cited by 11 publications

(1 citation statement)

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“…It is worth to mention that Cioabȃ in [6] investigated the relationship between edge-connectivity and adjacency eigenvalues of regular graphs. From then on, the edge-connectivity problem has been intensively studied by many researchers, as found in [1,6,7,11,12,16,17,18,19,21,22], among others. For the vertex-connectivity of graphs, one can refer to [1,14,20,23].…”

Section: Introductionmentioning

confidence: 99%

Connectivity and eigenvalues of graphs with given girth or clique number

Hong

Lai

Xia

2020

Preprint

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Let κ ′ (G), κ(G), µ n−1 (G) and µ 1 (G) denote the edge-connectivity, vertex-connectivity, the algebraic connectivity and the Laplacian spectral radius of G, respectively. In this paper, we prove that for integers k ≥ 2 and r ≥ 2, and any simple graph G of order n with minimum degree δ ≥ k, girth g ≥ 3 and clique number ω(G) ≤ r, the edge-connectivity, where N (δ, g) is the Moore bound on the smallest possible number of vertices such that there exists a δ-regular simple graph with girth g, and ϕ(δ, r) = max{δ + 1, ⌊ rδ r−1 ⌋}. Analogue results involving µ n−1 (G) and µ 1 (G) µ n−1 (G) to characterize vertex-connectivity of graphs with fixed girth and clique number are also presented. Former results in [

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