Given graph with set of vertex and set of edge . Set subset of is called domination set if every point in is adjacent with at least one point in in graph . The minimum cardinality of all set of domination graph is called domination number. Let be a subset of , set is called a neighborhood set if with induced subgraph of . The minimum cardinality of all the neighborhood set of graph is called the neighborhood number. There are several types of neighborhood domination number depending on the parameters. In this paper we examine the transversal neighborhood domination number and global neighborhood domination number in complete graph and complete bipartite graph.
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