# 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

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topJoanna 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

top- [1] J.A. Bondy and U.S.R. Murty: Graph Theory with Applications, Macmillan, London, 1976.
- [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] 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] 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] T.W. Haynes, S.T. Hedetniemi and P.J. Slater: Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998. Zbl0890.05002
- [6] S.T. Hedetniemi and R. Laskar: Connected domination in graphs, Graph Theory and Combinatorics, Academic Press, London, 1984, pp. 209–217.
- [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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