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{"references": ["1.\tJ. R. Griggs and J. P. Hutchinson, On the r-domination number of a graph, Discrete Mathematics, 101, (1992), 65-72. 2.\tT. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1997. 3.\tT. W. Haynes, S. T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998. 4.\tW. Imrich, S. Klav\u02c7zar, D. F. Rall: Topics in Graph Theory. A. K. Peters Ltd.,Wellesley, MA, 2008. 5.\tOre, Oystein, Theory of Graphs, No. 38, American Mathematical Soc., 1962. 6.\tN. 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.\tG. Yero, J. A. Rodr\u00b4\u0131guez-Vel\u00b4azquez, Roman domination in Cartesian product graphs and Cartesian product graph, Discrete Math. 7(2013), 262-274."]}
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.
Dominating Set, Distance Two Domination, Cartesian Product Graph & Subdivision Number
Dominating Set, Distance Two Domination, Cartesian Product Graph & Subdivision Number
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