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An upper bound for total domination subdivision numbers

Karami, H ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-010-0877-1
  3. Publisher: 2011
  4. Abstract:
  5. 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 γt(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sd γt (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 first prove that sdγt(G) < n -δ + 2 for every simple connected graph G of order n ≥ 3. We also classify all simple connected graphs G with sdγt (G) = n -δ+ 2,n-δ + 1, and n-δ
  6. Keywords:
  7. Total domination number ; Total domination subdivision number
  8. Source: Ars Combinatoria ; Volume 102 , February , 2011 , Pages 321-331 ; 03817032 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00373-010-0877-1