Trees with equal restrained domination and total restrained domination numbers

• Autorzy: Joanna Raczek
• Języki publikacji: EN

Abstrakty

EN

For a graph G = (V,E), a set D ⊆ V(G) is a total restrained dominating set if it is a dominating set and both ⟨D⟩ and ⟨V(G)-D⟩ do not have isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. A set D ⊆ V(G) is a restrained dominating set if it is a dominating set and ⟨V(G)-D⟩ does not contain an isolated vertex. The cardinality of a minimum restrained dominating set in G is the restrained domination number. We characterize all trees for which total restrained and restrained domination numbers are equal.

Słowa kluczowe

EN

total restrained domination number; restrained domination number; trees

Kategorie tematyczne

• 05C05: Trees
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 83-91

Daty

wydano

2007

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, S.T. Hedetniemi, R.C. Laskar and L.R. Marcus, Restrained domination in graphs, Discrete Math. 203 (1999) 61-69, doi: 10.1016/S0012-365X(99)00016-3.
• [2] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi and L.R. Marcus, Restrained domination in trees, Discrete Math. 211 (2000) 1-9, doi: 10.1016/S0012-365X(99)00036-9.
• [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, New York, 1998).
• [4] M.A. Henning, Trees with equal average domination and independent domination numbers, Ars Combin. 71 (2004) 305-318.
• [5] D. Ma, X. Chen and L. Sun, On total restrained domination in graphs, Czechoslovak Math. J. 55 (2005) 165-173, doi: 10.1007/s10587-005-0012-2.
• [6] J.A. Telle and A. Proskurowski, Algorithms for vertex partitioning problems on partial k-trees, SIAM J. Discrete Math. 10 (1997) 529-550, doi: 10.1137/S0895480194275825.

Identyfikatory

DOI

10.7151/dmgt.1346