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Exact $2$ -step domination in graphs

Gary Chartrand; Frank Harary; Moazzem Hossain; Kelly Schultz — 1995

Mathematica Bohemica

For a vertex $v$ in a graph $G$ , the set $N_{2} (v)$ consists of those vertices of $G$ whose distance from $v$ is 2. If a graph $G$ contains a set $S$ of vertices such that the sets $N_{2} (v)$ , $v \in S$ , form a partition of $V (G)$ , then $G$ is called a $2$ -step domination graph. We describe $2$ -step domination graphs possessing some prescribed property. In addition, all $2$ -step domination paths and cycles are determined.

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