# Graph domination in distance two

Gábor Bacsó; Attila Tálos; Zsolt Tuza

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 1-2, page 121-128
- ISSN: 2083-5892

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topGábor Bacsó, Attila Tálos, and Zsolt Tuza. "Graph domination in distance two." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 121-128. <http://eudml.org/doc/270765>.

@article{GáborBacsó2005,

abstract = {Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that $Dom Dom _u = Dom₂ _u$ holds for $_u$ = all connected graphs without induced $P_u$ (u ≥ 2). (In particular, ₂ = K₁ and ₃ = all complete graphs.) Some negative examples are also given.},

author = {Gábor Bacsó, Attila Tálos, Zsolt Tuza},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; dominating set; connected domination; distance domination; forbidden induced subgraph; -dominating subgraph},

language = {eng},

number = {1-2},

pages = {121-128},

title = {Graph domination in distance two},

url = {http://eudml.org/doc/270765},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Gábor Bacsó

AU - Attila Tálos

AU - Zsolt Tuza

TI - Graph domination in distance two

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 1-2

SP - 121

EP - 128

AB - Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that $Dom Dom _u = Dom₂ _u$ holds for $_u$ = all connected graphs without induced $P_u$ (u ≥ 2). (In particular, ₂ = K₁ and ₃ = all complete graphs.) Some negative examples are also given.

LA - eng

KW - graph; dominating set; connected domination; distance domination; forbidden induced subgraph; -dominating subgraph

UR - http://eudml.org/doc/270765

ER -

## References

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