# Graphs with equal domination and 2-distance domination numbers

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 2, page 375-385
- ISSN: 2083-5892

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topJoanna Raczek. "Graphs with equal domination and 2-distance domination numbers." Discussiones Mathematicae Graph Theory 31.2 (2011): 375-385. <http://eudml.org/doc/270826>.

@article{JoannaRaczek2011,

abstract = {Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum cardinality of a 2-distance dominating set of G. We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers.},

author = {Joanna Raczek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination number; trees; unicyclic graphs; distance domination number},

language = {eng},

number = {2},

pages = {375-385},

title = {Graphs with equal domination and 2-distance domination numbers},

url = {http://eudml.org/doc/270826},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Joanna Raczek

TI - Graphs with equal domination and 2-distance domination numbers

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 2

SP - 375

EP - 385

AB - Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum cardinality of a 2-distance dominating set of G. We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers.

LA - eng

KW - domination number; trees; unicyclic graphs; distance domination number

UR - http://eudml.org/doc/270826

ER -

## References

top- [1] M. Borowiecki and M. Kuzak, On the k-stable and k-dominating sets of graphs, in: Graphs, Hypergraphs and Block Systems. Proc. Symp. Zielona Góra 1976, ed. by M. Borowiecki, Z. Skupień, L. Szamkołowicz, (Zielona Góra, 1976). Zbl0344.05143
- [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker Inc., 1998). Zbl0890.05002

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