login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=3..79.

Jun-Ming 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 30 19:55 EST 2023. Contains 359947 sequences. (Running on oeis4.)