Abstract

The total domination subdivision number $\mathrm{sd}_{\gamma _{t}}(G)$ 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 $\mathrm{sd}_{\gamma_{t}}(G)\leq \lfloor\frac{2n}{3}\rfloor$ for any simple connected graph G of order n?3 other than K 4. We also determine all simple connected graphs G with $\mathrm{sd}_{\gamma_{t}}(G)=\lfloor\frac{2n}{3}\rfloor$ .

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