# Full domination in graphs

Robert C. Brigham; Gary Chartrand; Ronald D. Dutton; Ping Zhang

Discussiones Mathematicae Graph Theory (2001)

- Volume: 21, Issue: 1, page 43-62
- ISSN: 2083-5892

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topRobert C. Brigham, et al. "Full domination in graphs." Discussiones Mathematicae Graph Theory 21.1 (2001): 43-62. <http://eudml.org/doc/270252>.

@article{RobertC2001,

abstract = {For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_\{FH\}(G)$. A full dominating set of G of cardinality $γ_\{FH\}(G)$ is called a $γ_\{FH\}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.},

author = {Robert C. Brigham, Gary Chartrand, Ronald D. Dutton, Ping Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {full domination; full star domination; full closed domination; full open domination; full domination number; full star domination number; full closed domination number; full open domination number},

language = {eng},

number = {1},

pages = {43-62},

title = {Full domination in graphs},

url = {http://eudml.org/doc/270252},

volume = {21},

year = {2001},

}

TY - JOUR

AU - Robert C. Brigham

AU - Gary Chartrand

AU - Ronald D. Dutton

AU - Ping Zhang

TI - Full domination in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2001

VL - 21

IS - 1

SP - 43

EP - 62

AB - For each vertex v in a graph G, let there be associated a subgraph $H_v$ of G. The vertex v is said to dominate $H_v$ as well as dominate each vertex and edge of $H_v$. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number $γ_{FH}(G)$. A full dominating set of G of cardinality $γ_{FH}(G)$ is called a $γ_{FH}$-set of G. We study three types of full domination in graphs: full star domination, where $H_v$ is the maximum star centered at v, full closed domination, where $H_v$ is the subgraph induced by the closed neighborhood of v, and full open domination, where $H_v$ is the subgraph induced by the open neighborhood of v.

LA - eng

KW - full domination; full star domination; full closed domination; full open domination; full domination number; full star domination number; full closed domination number; full open domination number

UR - http://eudml.org/doc/270252

ER -

## References

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- [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
- [4] S.R. Jayaram, Y.H.H. Kwong and H.J. Straight, Neighborhood sets in graphs, Indian J. Pure Appl. Math. 22 (1991) 259-268. Zbl0733.05074
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- [6] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38 (Amer. Math. Soc. Providence, RI, 1962).

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