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Discussiones Mathematicae Graph Theory 31(3) (2011) 475-491
DOI: https://doi.org/10.7151/dmgt.1559

BOUNDING NEIGHBOR-CONNECTIVITY OF ABELIAN CAYLEY GRAPHS

Lynne L. Doty

Mathematics Department
Marist College
Poughkeepsie, NY 12601, USA
e-mail: Lynne.Doty@marist.edu

Abstract

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.

Keywords: Cayley graphs, neighbor-connectivity bound.

2010 Mathematics Subject Classification: 05C25, 05C40.

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Received 2 September 2009
Revised 5 May 2010
Accepted 17 May 2010