Bounding the total domination subdivision number of a graph in terms of its order
The total domination subdivision number sd(gamma t) ( G) of a graph G is the minimum number of edges that must be subdivided ( each edge in G can be subdivided at most once) in order to increase the total domination number. In this paper we prove that sd(gamma t) ( G)  = 3 other than K-4. We also determine all simple connected graphs G with sd(gamma t) ( G) = left perpendicular2n/3right perpendicular.
total domination subdivision number total domination number