# Exact $2$-step domination in graphs

Gary Chartrand; Frank Harary; Moazzem Hossain; Kelly Schultz

Mathematica Bohemica (1995)

- Volume: 120, Issue: 2, page 125-134
- ISSN: 0862-7959

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topChartrand, Gary, et al. "Exact $2$-step domination in graphs." Mathematica Bohemica 120.2 (1995): 125-134. <http://eudml.org/doc/247782>.

@article{Chartrand1995,

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.},

author = {Chartrand, Gary, Harary, Frank, Hossain, Moazzem, Schultz, Kelly},

journal = {Mathematica Bohemica},

keywords = {$2$-step domination graph; paths; cycles; 2-step domination; paths; cycles},

language = {eng},

number = {2},

pages = {125-134},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Exact $2$-step domination in graphs},

url = {http://eudml.org/doc/247782},

volume = {120},

year = {1995},

}

TY - JOUR

AU - Chartrand, Gary

AU - Harary, Frank

AU - Hossain, Moazzem

AU - Schultz, Kelly

TI - Exact $2$-step domination in graphs

JO - Mathematica Bohemica

PY - 1995

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 120

IS - 2

SP - 125

EP - 134

AB - 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.

LA - eng

KW - $2$-step domination graph; paths; cycles; 2-step domination; paths; cycles

UR - http://eudml.org/doc/247782

ER -

## References

top- G. Chartrand, L. Lesniak, Graphs & Digraphs, (second edition). Wadsworth k. Brooks/Cole, Monterey, 1986. (1986) Zbl0666.05001MR0834583
- F. Harary, Graph Theory, Addison-Wesley, Reading, 1969. (1969) Zbl0196.27202MR0256911

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