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 A182215 Bondage number of the Cartesian product graph G = C_n X C_3. 0

%I #6 Apr 19 2012 16:06:28

%S 2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,

%T 4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,

%U 2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5,2,4,4,5

%N Bondage number of the Cartesian product graph G = C_n X C_3.

%C Theorem 5.1.2 of Xu, and proved in Sohn, 2007. The bondage number of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number of G.

%D M. Y. Sohn, X.-D. Yuan and H. S. Jeong, The bondage number of C_3 X C_n. Journal of the Korean Mathematical Society, 44(6) (2007), 1213-1231

%H Jun-Ming Xu, <a href="http://arxiv.org/abs/1204.4010">On Bondage Numbers of Graphs -- a survey with some comments</a>, arXiv:1204.4010v1 [math.CO], Apr 18 2012

%F For n>=4 a(n) = bondage number b(C_n X C_3) = 2 if n = 0 (mod 4), 4 if n = 1 or 2 (mod 4), 5 if n = 3 (mod 4).

%Y Cf. A182214.

%K nonn,easy

%O 4,1

%A _Jonathan Vos Post_, Apr 19 2012

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