The Nonsplit Bondage Number of Graphs

Authors

  • Chrislight RJ Dept. of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai - 627 002, Tamil Nadu, INDIA
  • Mary YTS Dept. of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai - 627 002, Tamil Nadu, INDIA

Keywords:

Nonsplit dominating set, Nonsplit domination number, Bondage number, Nonsplit bondage number

Abstract

A set of vertices in a graph is a nonsplit dominating set if the induced subgraph is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number of and denoted . In this paper, we define the nonsplit bondage number of a graph to be the minimum cardinality of a set of edges for which . We obtain sharp bounds for and obtain the exact values for some standard graphs.

References

[1] J. F. Fink, M. S. Jacobson, L. F. Kinch and J. Roberts, The Bondage number of a graph, Discrete Math. 86(1990) 47-57.

[2] F. Harary, Graph Theory, Addision-Wesley, Reading Mass. (1969).

[3] L. Hartnell, Douglas F. Rall, Bounds on the bondage number of a graph, Discrete Mathematics 128 (1994) 173-177.

[4] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Disc.Math., Marcel Dekker, Inc., New York, 1998.

[5] V. R. Kulli and B. Janakiram, The Nonsplit Domination Number of a Graph, Indian J.Pure appl. Math., 31(4):441-447, April 2000.

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Published

2025-11-25

How to Cite

[1]
R. J. Chrislight and Y. T. S. Mary, “The Nonsplit Bondage Number of Graphs”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 74–76, Nov. 2025.

Issue

Vol. 7 No. 5 (2019): IJCSE Special Issue Mar Edition

Section

Research Article

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