

A182214


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


1



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, 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, 3, 2, 2, 4, 3, 2, 2, 4, 3
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OFFSET

3,1


COMMENTS

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.


REFERENCES

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. 471489.


LINKS

Table of n, a(n) for n=3..79.
JunMing Xu, On Bondage Numbers of Graphs  a survey with some comments, arXiv:1204.4010v1 [math.CO], Apr 18 2012


FORMULA

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).


CROSSREFS

Sequence in context: A141862 A237612 A111739 * A339505 A351163 A216161
Adjacent sequences: A182211 A182212 A182213 * A182215 A182216 A182217


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Apr 19 2012


STATUS

approved



