Bounding the total domination subdivision number of a graph in terms of its order

Odile Favaron (), Hossein Karami and Seyyed Mahmoud Sheikholeslami ()
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Odile Favaron: Univ. Paris-Sud
Hossein Karami: Azarbaijan University of Tarbiat Moallem
Seyyed Mahmoud Sheikholeslami: Azarbaijan University of Tarbiat Moallem

Journal of Combinatorial Optimization, 2011, vol. 21, issue 2, No 4, 209-218

Abstract: 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 $\mathrm{sd}_{\gamma_{t}}(G)=\lfloor\frac{2n}{3}\rfloor$ .

Keywords: Total domination number; Total domination subdivision number (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-009-9224-y

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