2013/09/27 by Diana Avella-Alaminos, Magda Dettlaff, Avella-Alaminos, Diana +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1309.7228
15 pages, 1 figure, 9 references
arxiv created 2013/09/27 · arxiv updated 2013/09/30
The domination multisubdivision number of a nonempty graph G was defined 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 multisubdivision 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.