Graphs with equal domination and 2-distance domination numbers

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

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Abstract

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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.

How to cite

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Joanna 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

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1. [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. [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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