Discussiones Mathematicae Graph Theory 31(3) (2011)
475-491
doi: 10.7151/dmgt.1559
Lynne L. Doty
Mathematics Department
Marist College
Poughkeepsie, NY 12601, USA
e-mail: Lynne.Doty@marist.edu
Keywords: Cayley graphs, neighbor-connectivity bound.
2010 Mathematics Subject Classification: 05C25, 05C40.
[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. |
Received 2 September 2009
Revised 5 May 2010
Accepted 17 May 2010