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• # Artykuł - szczegóły

## Open Mathematics

2006 | 4 | 1 | 34-45

## On the doubly connected domination number of a graph

EN

### Abstrakty

EN
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.

EN

34-45

wydano
2006-03-01
online
2006-03-01

### Twórcy

autor
• Gdańsk University of Technology
autor
• Gdańsk University of Technology
autor
• Gdańsk University of Technology

### Bibliografia

• [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.
• [4] M.R. Garey and D.S. Johnson: Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979.
• [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater: Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
• [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.