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On the total domination subdivision number in some classes of graphs

Author

Listed:
  • 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)

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.

Suggested Citation

  • O. Favaron & H. Karami & R. Khoeilar & S. M. Sheikholeslami, 2010. "On the total domination subdivision number in some classes of graphs," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 76-84, July.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:1:d:10.1007_s10878-008-9193-6
    DOI: 10.1007/s10878-008-9193-6
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