# 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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- [7] P. Erdős, M. Saks and V.T. Sós Maximum induced trees in graphs, J. Combin. Theory (B) 41 (1986) 61-79, doi: 10.1016/0095-8956(86)90028-6. Zbl0603.05023
- [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, N.Y., 1998). Zbl0890.05002
- [9] E.S. Wolk, The comparability graph of a tree, Proc. Amer. Nath. Soc. 3 (1962) 789-795, doi: 10.1090/S0002-9939-1962-0172273-0. Zbl0109.16402
- [10] - Topics on Domination (R. Laskar and S. Hedetniemi, eds.), Annals of Discrete Math. 86 (1990).

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