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

Abstract

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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 D o m D o m u = D o m ₂ 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.

How to cite

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Gábor 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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  8. [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. [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
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