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Abstrakty
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.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
109-119
Opis fizyczny
Daty
wydano
2008
otrzymano
2006-11-10
poprawiono
2007-12-18
zaakceptowano
2007-12-18
Twórcy
autor
- 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1395