Weakly connected domination subdivision numbers

Joanna Raczek

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 1, page 109-119
  • ISSN: 2083-5892

Abstract

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A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.

How to cite

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Joanna Raczek. "Weakly connected domination subdivision numbers." Discussiones Mathematicae Graph Theory 28.1 (2008): 109-119. <http://eudml.org/doc/270581>.

@article{JoannaRaczek2008,
abstract = {A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.},
author = {Joanna Raczek},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {weakly connected domination number; weakly connected domination subdivision number},
language = {eng},
number = {1},
pages = {109-119},
title = {Weakly connected domination subdivision numbers},
url = {http://eudml.org/doc/270581},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Joanna Raczek
TI - Weakly connected domination subdivision numbers
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 1
SP - 109
EP - 119
AB - A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.
LA - eng
KW - weakly connected domination number; weakly connected domination subdivision number
UR - http://eudml.org/doc/270581
ER -

References

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  1. [1] G.S. Domke, J.H. Hattingh and L.R. Marcus, On weakly connected domination in graphs II, Discrete Math. 305 (2005) 112-122, doi: 10.1016/j.disc.2005.10.006. Zbl1078.05064
  2. [2] J.E. Dunbar, J.W. Grossman, J.H. Hattingh, S.T. Hedetniemi and A.A. McRae, On weakly connected domination in graphs, Discrete Math. 167/168 (1997) 261-269, doi: 10.1016/S0012-365X(96)00233-6. Zbl0871.05037
  3. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker Inc., New York, 1998). Zbl0890.05002
  4. [4] T.W. Haynes, M.A. Henning and L.S. Hopkins, Total domination subdivision numbers of graphs, Discuss. Math. Graph Theory 24 (2003) 457-467, doi: 10.7151/dmgt.1244. Zbl1065.05070
  5. [5] J.H. Hattingh, E. Jonck and L.R. Marcus, A note on the weakly connected subdivision number of a graph (2007), to appear. 

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