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Keywords:
$2$-step domination graph; paths; cycles
$2$-step domination graph; paths; cycles
Summary:
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.
References:
[1] G. Chartrand, L. Lesniak: Graphs & Digraphs. (second edition). Wadsworth k. Brooks/Cole, Monterey, 1986. MR 0834583 | Zbl 0666.05001
[2] F. Harary: Graph Theory. Addison-Wesley, Reading, 1969. MR 0256911 | Zbl 0196.27202
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