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$2$-step domination graph; paths; cycles
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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[2] F. Harary: Graph Theory. Addison-Wesley, Reading, 1969. MR 0256911 | Zbl 0196.27202
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