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Discussiones Mathematicae Graph Theory 24(3) (2004) 457-467
DOI: https://doi.org/10.7151/dmgt.1244

TOTAL DOMINATION SUBDIVISION NUMBERS OF GRAPHS

Teresa W. Haynes Department of Mathematics East Tennessee State University Johnson City, TN 37614-0002 USA

Michael A. Henning School of Mathematics, Statistics and Information Technology, University of Natal Pietermaritzburg, 3209 South Africa

Lora S. Hopkins Department of Mathematics East Tennessee State University Johnson City, TN 37614-0002 USA

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.

Keywords: total domination number, total domination subdivision number.

2000 Mathematics Subject Classification: 05C69.

References

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Received 2 June 2003
Revised 29 September 2003