Bounding neighbor-connectivity of Abelian Cayley graphs

• Autorzy: Lynne L. Doty
• Języki publikacji: EN

Abstrakty

EN

For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately (1/2)κ. The main result of this paper is the constructive development of an alternative, and often tighter, bound for abelian Cayley graphs through the use of an auxiliary graph determined by the generating set of the abelian Cayley graph.

Słowa kluczowe

EN

Cayley graphs; neighbor-connectivity bound

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
• 05C40: Connectivity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2011
• Tom: 31
• Numer: 3
• Strony: 475-491

Daty

wydano

2011

otrzymano

2009-09-02

poprawiono

2010-05-05

zaakceptowano

2010-05-17

Twórcy

autor

Lynne L. Doty

• Mathematics Department, Marist College, Poughkeepsie, NY 12601, USA

Bibliografia

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• [8] G. Gunther, B. Hartnell and R. Nowakowski, Neighbor-connected graphs and projective planes, Networks 17 (1987) 241-247, doi: 10.1002/net.3230170208.
• [9] J. Huang and J.-M. Xu, The bondage numbers and efficient dominations of vertex-transitive graphs, Discrete Math. 308 (2008) 571-582, doi: 10.1016/j.disc.2007.03.027.
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Identyfikatory

DOI

10.7151/dmgt.1559