Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

Balbuena, C.; Cera, M.; Diánez, A.; García–Vázquez, P.; Marcote, X.

doi:10.1016/j.disc.2007.07.012

Cited by 13 publications

(4 citation statements)

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“…A sharper measure of network vulnerability is given by the notion of extraconnectivity introduced by Fàbrega and Fiol [12]. Extraconnectivity was investigated by Fàbrega and Fiol [13], by Balbuena et al [4], by Balbuena [1], and more recently by Balbuena et al [6]. Also the concept of k-isoperimetric numbers (or k-isoperimetric connectivity) introduced by Hamidoune in [19] provides another sharper measure of network vulnerability.…”

Section: Introductionmentioning

confidence: 99%

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

2011

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A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let be a vertex-transitive graph of degree d with order at least d +4. We give necessary and sufficient conditions for the vosperianity of . Moreover, assuming that distinct vertices have distinct neighbors, we show that is vosperian if and only if it is superconnected. Let G be a group and let

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Section: Introductionmentioning

confidence: 99%

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

2011

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“…Fàbrega and Fiol also proposed the concept of p -restricted (vertex-)connectivity κ p and some results for this kind of connectivity have been obtained in [2,3,27,29] . Other kind of connectivity measures involving both vertices and edges are studied in [11,19] , for instance.…”

Section: Article In Pressmentioning

confidence: 99%

The p-restricted edge-connectivity of Kneser graphs

Balbuena

Marcote

2019

Applied Mathematics and Computation

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“…Some related work on lower bounds for λ k (G), as well as its vertex counterpart κ k (G), under certain constraints on the diameter and the girth can be found in [1][2][3]12].…”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions for a graph to be λ_k‐optimal with given girth and diameter

Zhang

Liu

2009

Networks

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Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

Cited by 13 publications

References 13 publications

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

The p-restricted edge-connectivity of Kneser graphs

Sufficient conditions for a graph to be λ_k‐optimal with given girth and diameter

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Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

Cited by 13 publications

References 13 publications

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

The p-restricted edge-connectivity of Kneser graphs

Sufficient conditions for a graph to be λk‐optimal with given girth and diameter

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Sufficient conditions for a graph to be λ_k‐optimal with given girth and diameter