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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
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. 471-489.
LINKS
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: A111739 A376310 A372490 * A339505 A373012 A351163
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Apr 19 2012
STATUS
approved