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Total Domination Multisubdivision Number of a Graph

Diana Avella-AlaminosMagda DettlaffMagdalena LemańskaRita Zuazua — 2015

Discussiones Mathematicae Graph Theory

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...

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