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## Discussiones Mathematicae Graph Theory

2004 | 24 | 3 | 457-467
Tytuł artykułu

### Total domination subdivision numbers of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A set S of vertices in a graph G = (V,E) is a total dominating set of G if every vertex of V is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. The total domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the total domination number. First we establish bounds on the total domination subdivision number for some families of graphs. Then we show that the total domination subdivision number of a graph can be arbitrarily large.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
457-467
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-06-02
poprawiono
2003-09-29
Twórcy
autor
• Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002 USA
autor
• School of Mathematics, Statistics and Information Technology, University of Natal, Pietermaritzburg, 3209 South Africa
autor
• Department of Mathematics, East Tennessee State University, Johnson City, TN 37614-0002 USA
Bibliografia
• [1] S. Arumugam, private communication, June, 2000.
• [2] E.J. Cockayne, R.M. Dawes, and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304.
• [3] O. Favaron, T.W. Haynes, and S.T. Hedetniemi, Domination subdivision numbers in graphs, submitted for publication.
• [4] T.W. Haynes, S.M. Hedetniemi, and S.T. Hedetniemi, Domination and independence subdivision numbers of graphs, Discuss. Math. Graph Theory 20 (2000) 271-280, doi: 10.7151/dmgt.1126.
• [5] T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, D.P. Jacobs, J. Knisely, and L.C. van der Merwe, Domination subdivision numbers, Discuss. Math. Graph Theory 21 (2001) 239-253, doi: 10.7151/dmgt.1147.
• [6] T.W. Haynes, M.A. Henning, and L.S. Hopkins, Total domination subdivision numbers in trees, submitted for publication.
• [7] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [8] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
• [9] T.W. Haynes, S.T. Hedetniemi, and L.C. van der Merwe, Total domination subdivision numbers, J. Combin. Math. Combin. Comput. 44 (2003) 115-128.
Typ dokumentu
Bibliografia
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