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Total Domination Multisubdivision Number of a Graph

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Avella-Alaminos D., Dettlaff M., Lemańska M., Zuazua R.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

315-327

The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msdγt (G) of a graph G and we show that for any connected graph G of order at least two, msdγt (G) ≤ 3. We show that for trees the total domination multisubdi- vision number is equal to the known total domination subdivision number. We also determine the total domination multisubdivision number for some classes of graphs and characterize trees T with msdγt (T) = 1.

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1 Discussiones Mathematicae Graph Theory

1 Avella-Alaminos D.

1 Dettlaff M.

1 Lemańska M.

1 Zuazua R.

1 2015

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Total Domination Multisubdivision Number of a Graph