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## Sunday, April 11, 2021

Given graph $G$ with set of vertex $V$ and set of edge $E$. Set $D$ subset of $V$ is called domination set if every point in $V - D$ is adjacent with at least one point in $D$ in graph $G$. The minimum cardinality of all set of domination graph $G$ is called domination number. Let $S$ be a subset of $V$, set $S$ is called a neighborhood set if $G=\bigcup_{v \in S}^{}\left \langle N(v) \right \rangle$ with $\left \langle N(v) \right \rangle$ induced subgraph $G$ of $N(v)$. The minimum cardinality of all the neighborhood set of graph $G$ 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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