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

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, 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, 2, 4, 4, 5, 2, 4, 4, 5, 2, 4, 4, 5, 2, 4, 4, 5, 2, 4, 4, 5

Offset

4,1

Comments

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.

References

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

Links

Table of n, a(n) for n=4..91.

Jun-Ming Xu, On Bondage Numbers of Graphs -- a survey with some comments, arXiv:1204.4010v1 [math.CO], Apr 18 2012

Formula

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).

Crossrefs

Cf. A182214.

Sequence in context: A009622 A232845 A269300 * A036443 A036437 A053306

Adjacent sequences: A182212 A182213 A182214 * A182216 A182217 A182218

Keyword

nonn,easy

Author

Jonathan Vos Post, Apr 19 2012

Status

approved