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2011 | 31 | 3 | 475-491
Tytuł artykułu

Bounding neighbor-connectivity of Abelian Cayley graphs

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Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
31
Numer
3
Strony
475-491
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-09-02
poprawiono
2010-05-05
zaakceptowano
2010-05-17
Twórcy
  • Mathematics Department, Marist College, Poughkeepsie, NY 12601, USA
Bibliografia
  • [1] I.J. Dejter and O. Serra, Efficient dominating sets in Cayley graphs, Discrete Appl. Math. 129 (2003) 319-328, doi: 10.1016/S0166-218X(02)00573-5.
  • [2] L.L. Doty, A new bound for neighbor-connectivty of abelian Cayley graphs, Discrete Math. 306 (2006) 1301-1316, doi: 10.1016/j.disc.2005.09.018.
  • [3] L.L. Doty, R.J. Goldstone and C.L. Suffel, Cayley graphs with neighbor connectivity one, SIAM J. Discrete Math. 9 (1996) 625-642, doi: 10.1137/S0895480194265751.
  • [4] R.J. Goldstone, The structure of neighbor disconnected vertex transitive graphs, Discrete Math. 202 (1999) 73-100, doi: 10.1016/S0012-365X(98)00348-3.
  • [5] G. Gunther, Neighbour-connectivity in regular graphs, Discrete Appl. Math. 11 (1985) 233-243, doi: 10.1016/0166-218X(85)90075-7.
  • [6] G. Gunther and B. Hartnell, On minimizing the effects of betrayals in a resistance movement, in: Proc. 8th Manitoba Conf. on Numerical Mathematics and Computing (Winnipeg, Manitoba, Canada, 1978) 285-306.
  • [7] G. Gunther and B. Hartnell, Optimal k-secure graphs, Discrete Appl. Math. 2 (1980) 225-231, doi: 10.1016/0166-218X(80)90042-6.
  • [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.
  • [10] N. Obradovic, J. Peters and G. Ruzic, Efficient domination in circulant graphs with two chord lengths, Information Processing Letters 102 (2007) 253-258, doi: 10.1016/j.ipl.2007.02.004.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1559
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