Geodesic
Exact $2$-step domination in graphs
Mathematica Bohemica, Tome 120 (1995) no. 2, pp. 125-134

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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.
DOI : 10.21136/MB.1995.126228
Classification : 05C12, 05C38, 05C70
Keywords: $2$-step domination graph; paths; cycles 
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Chartrand, Gary; Harary, Frank; Hossain, Moazzem; Schultz, Kelly. Exact $2$-step domination in graphs. Mathematica Bohemica, Tome 120 (1995) no. 2, pp. 125-134. doi: 10.21136/MB.1995.126228

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