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Total domination and total domination subdivision numbers

Favaron, O ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. Publisher: 2007
  3. Abstract:
  4. 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<(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt(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. We show that sdγt(G) ≤ n - γt(G) + 1 for any graph G of order n ≥ 3 and that sdγt(G) < n-γt(G) except if G ≃ P3, C3, K4, P6 or C6
  5. Keywords:
  6. Total outer-connected domination number ; Total outer-connected domination subdivision number ; GRAPHS ; Graph G
  7. Source: Australasian Journal of Combinatorics ; Volume 38 , 2007 , Pages 229-235 ; 10344942 (ISSN)
  8. URL: https://www.worldscientific.com/doi/abs/10.1142/S1793830913500092