On the total domination subdivision number in some classes of graphs

O. Favaron (), H. Karami, R. Khoeilar and S. M. Sheikholeslami ()
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O. Favaron: Univ. Paris Sud and CNRS
H. Karami: Azarbaijan University of Tarbiat Moallem
R. Khoeilar: Azarbaijan University of Tarbiat Moallem
S. M. Sheikholeslami: Azarbaijan University of Tarbiat Moallem

Journal of Combinatorial Optimization, 2010, vol. 20, issue 1, No 5, 76-84

Abstract: Abstract A set S of vertices of a graph G=(V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $\mathrm {sd}_{\gamma_{t}}(G)$ 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 $\mathrm {sd}_{\gamma_{t}}(G)\leq\gamma_{t}(G)+1$ for some classes of graphs.

Keywords: Total domination number; Total domination subdivision number (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10878-008-9193-6

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