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MATHEMATICA BOHEMICA, Vol. 120, No. 2, pp. 125-134, 1995
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Exact $2$-step domination in graphs

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Gary Chartrand, Frank Harary, Moazzem Hossain, Kelly Schultz

G. Chartrand, K. Schultz, Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008-5152; F. Harary, Department of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003; M. Hossain, Compass Design Automation, M/S 410, 1865 Lundi Ave., San Jose, California 95131

**Abstract:** 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.

**Keywords:** $2$-step domination graph

**Classification (MSC91):** 05C38

**Full text of the article:**

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