On the doubly connected domination number of a graph

Joanna Cyman; Magdalena Lemańska; Joanna Raczek

Open Mathematics (2006)

  • Volume: 4, Issue: 1, page 34-45
  • ISSN: 2391-5455

Abstract

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For a given connected graph G = (V, E), a set D ⊆ V ( G ) is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number. We investigate several properties of doubly connected dominating sets and give some bounds on the doubly connected domination number.

How to cite

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Joanna Cyman, Magdalena Lemańska, and Joanna Raczek. "On the doubly connected domination number of a graph." Open Mathematics 4.1 (2006): 34-45. <http://eudml.org/doc/268934>.

@article{JoannaCyman2006,
abstract = {For a given connected graph G = (V, E), a set \[D \subseteq V(G)\] is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number. We investigate several properties of doubly connected dominating sets and give some bounds on the doubly connected domination number.},
author = {Joanna Cyman, Magdalena Lemańska, Joanna Raczek},
journal = {Open Mathematics},
keywords = {05C69},
language = {eng},
number = {1},
pages = {34-45},
title = {On the doubly connected domination number of a graph},
url = {http://eudml.org/doc/268934},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Joanna Cyman
AU - Magdalena Lemańska
AU - Joanna Raczek
TI - On the doubly connected domination number of a graph
JO - Open Mathematics
PY - 2006
VL - 4
IS - 1
SP - 34
EP - 45
AB - For a given connected graph G = (V, E), a set \[D \subseteq V(G)\] is a doubly connected dominating set if it is dominating and both 〈D〉 and 〈V (G)-D〉 are connected. The cardinality of the minimum doubly connected dominating set in G is the doubly connected domination number. We investigate several properties of doubly connected dominating sets and give some bounds on the doubly connected domination number.
LA - eng
KW - 05C69
UR - http://eudml.org/doc/268934
ER -

References

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  1. [1] J.A. Bondy and U.S.R. Murty: Graph Theory with Applications, Macmillan, London, 1976. 
  2. [2] C. Bo and B. Liu: “Some inequalities about connected domination number”, Disc. Math., Vol. 159, (1996), pp. 241–245. http://dx.doi.org/10.1016/0012-365X(95)00088-E 
  3. [3] P. Duchet and H. Meyniel: “On Hadwiger's number and the stability number”, Ann. Disc. Math., Vol. 13, (1982), pp. 71–74. Zbl0522.05060
  4. [4] M.R. Garey and D.S. Johnson: Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979. Zbl0411.68039
  5. [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater: Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. Zbl0890.05002
  6. [6] S.T. Hedetniemi and R. Laskar: Connected domination in graphs, Graph Theory and Combinatorics, Academic Press, London, 1984, pp. 209–217. 
  7. [7] E. Sampathkumar and H.B. Walikar: “The connected domination number of a graph”, J. Math. Phys. Sci., Vol. 13, (1979), pp. 607–613. Zbl0449.05057

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