Connectivity of vertex and edge transitive graphs

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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“…Notice that this result is also a basic tool in the work of Meng [31] and Meng and Zhang [32]. We recall here some simple preliminary lemmas.…”

Section: If H Is a 1-atom Of Cay(g S) Containing 1 Then H Is A Subgmentioning

confidence: 87%

“…Note that, a vosperian graph is superconnected. As observed by Meng [31], the notion of a vosperian graph coincide with the notion of a hyperconnected graph, introduced independently by Boesch [8], if |V| = d +3.…”

Section: Introductionmentioning

confidence: 96%

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

2011

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“…For instance, Meng [12] characterized non-super-connected vertex-and edge-transitive graphs, and Zhang and Meng [21] characterized non-super-connected edge-transitive graphs. Boesch et al [4,14] proved that the only connected edge-transitive graphs which are not super edge-connected are the cycles C n .…”

Section: An Interconnection Network Is Often Modeled As a Graph G Whmentioning

confidence: 99%

Super-connected but not super edge-connected graphs

Zhou

Feng

2010

Information Processing Letters

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“…In [7], Meng characterized vertex and edge transitive hyper-connected graphs. In [10], Zhang and Meng characterized edge transitive semi-hyper-connected graphs.…”

Section: Introduction and Notationmentioning

confidence: 99%