Published February 10, 2017
| Version v1
Journal article
Open
RESULTS ON DISTANCE-2 DOMINATION SUBDIVISION NUMBER OF CARTESIAN PRODUCT GRAPH
Creators
- 1. Department of Mathematics, Shri Andal Alagar College of Engineering, Mamandur, Kancheepuram, Tamilnadu
- 2. Research Centre, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur, Tamilnadu
Description
Let be a simple graph on the vertex set . In a graph G, A set is a dominating set of G if every vertex in is adjacent to some vertex in D. The bondage number of a graph [ is the cardinality of a smallest set of edges whose removal results in a graph with domination number larger than that of . A set is called a distance k dominating set of if every vertex in is with in distance of at least one vertex in , that is, for every vertex , there exists a vertex such that . In this paper we determine the domination number of Cartesian product graph in distance two dominating set and also find the subdivision number for Cartesian product graph.
Files
ICATAM-015.PDF
Files
(815.5 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:97a72750b973ec578c8b78f63643c760
|
815.5 kB | Preview Download |
Additional details
References
- 1. J. R. Griggs and J. P. Hutchinson, On the r-domination number of a graph, Discrete Mathematics, 101, (1992), 65-72. 2. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1997. 3. T. W. Haynes, S. T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998. 4. W. Imrich, S. Klavˇzar, D. F. Rall: Topics in Graph Theory. A. K. Peters Ltd.,Wellesley, MA, 2008. 5. Ore, Oystein, Theory of Graphs, No. 38, American Mathematical Soc., 1962. 6. N. Sridharan, V.S.A. Subramanian and M.D. Elias, Bounds on the Distance Two-Domination Number of a Graph, Graphs and Combinatorics, 18(3), (2002), 667-675. 7. G. Yero, J. A. Rodr´ıguez-Vel´azquez, Roman domination in Cartesian product graphs and Cartesian product graph, Discrete Math. 7(2013), 262-274.