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A182214 Bondage number of the Cartesian product graph G = C_n X K_2. 1


%S 3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,

%T 2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,3,2,2,4,

%U 3,2,2,4,3,2,2,4,3

%N Bondage number of the Cartesian product graph G = C_n X K_2.

%C Theorem 5.1.1 of Xu, and proved in Dunbar, 1998. 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 J. E. Dunbar, T. W. Haynes, U. Teschner, L. Volkmann, Bondage, insensitivity, and reinforcement. Domination in Graphs: Advanced Topics (T. W. Haynes, S. T. Hedetniemi, P. J. Slater eds.), Monogr. Textbooks Pure Appl. Math., 209, Marcel Dekker, New York, 1998, pp. 471-489.

%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 Let G = C_n X K_2, for n >= 3. Then a(n) = bondage number of G = 2 if n = 0 or 1 (mod 4), 3 if n = 3 (mod 4), 4 if n = 2 (mod 4).

%K nonn,easy

%O 3,1

%A _Jonathan Vos Post_, Apr 19 2012

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