# Total domination subdivision numbers of graphs

Teresa W. Haynes; Michael A. Henning; Lora S. Hopkins

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 3, page 457-467
- ISSN: 2083-5892

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topTeresa W. Haynes, Michael A. Henning, and Lora S. Hopkins. "Total domination subdivision numbers of graphs." Discussiones Mathematicae Graph Theory 24.3 (2004): 457-467. <http://eudml.org/doc/270656>.

@article{TeresaW2004,

abstract = {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.},

author = {Teresa W. Haynes, Michael A. Henning, Lora S. Hopkins},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total domination number; total domination subdivision number},

language = {eng},

number = {3},

pages = {457-467},

title = {Total domination subdivision numbers of graphs},

url = {http://eudml.org/doc/270656},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Teresa W. Haynes

AU - Michael A. Henning

AU - Lora S. Hopkins

TI - Total domination subdivision numbers of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 3

SP - 457

EP - 467

AB - 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.

LA - eng

KW - total domination number; total domination subdivision number

UR - http://eudml.org/doc/270656

ER -

## References

top- [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. Zbl0447.05039
- [3] O. Favaron, T.W. Haynes, and S.T. Hedetniemi, Domination subdivision numbers in graphs, submitted for publication. Zbl1071.05057
- [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. Zbl0984.05066
- [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. Zbl1006.05042
- [6] T.W. Haynes, M.A. Henning, and L.S. Hopkins, Total domination subdivision numbers in trees, submitted for publication. Zbl1054.05076
- [7] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [8] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
- [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. Zbl1020.05048

## Citations in EuDML Documents

top- Seyed Sheikholeslami, On the total domination subdivision numbers in graphs
- Diana Avella-Alaminos, Magda Dettlaff, Magdalena Lemańska, Rita Zuazua, Total Domination Multisubdivision Number of a Graph
- Joanna Raczek, Weakly connected domination subdivision numbers
- Odile Favaron, Hossein Karami, Rana Khoeilar, Seyed Mahmoud Sheikholeslami, Matchings and total domination subdivision number in graphs with few induced 4-cycles
- Vladimir D. Samodivkin, Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces

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