Weakly connected domination subdivision numbers

• Autorzy: Joanna Raczek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

weakly connected domination number; weakly connected domination subdivision number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 109-119

Daty

wydano

2008

otrzymano

2006-11-10

poprawiono

2007-12-18

zaakceptowano

2007-12-18

Twórcy

autor

Joanna Raczek

• Department of Discrete Mathematics, Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland

Bibliografia

• [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.
• [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.
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker Inc., New York, 1998).
• [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.
• [5] J.H. Hattingh, E. Jonck and L.R. Marcus, A note on the weakly connected subdivision number of a graph (2007), to appear.

Identyfikatory

DOI

10.7151/dmgt.1395