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Total Domination Number in Graphs

Gorzin, Ali Asghar | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46568 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Akbari, Saeed
  7. Abstract:
  8. In this dissertation we aim to survey the concepts and results concerning Total Domination Set. Consider graph G = (V;E). Let S be a subset of V . S is Total Domination Set in G if every vertex in V is adjacent to at least one vertex in S.Furthermore, we call S a k-Total Domination Set if every vertex in V is adjacent to at least k vertices in S. The size of the smallest Total Domination and k-Total Domination Set in a graph G is respectively called the Total Domination and k-Total Domination Number of G.Now, if there is a sequence of subsets of V like S = V0; V1; V2; : : : ; Vl = V so that for each i, every vertex in Vi is connected to at least k vertices in Vi1, S is a Dynamical k-Total Domination Set in G. The size of the smallest Dyanmical k-total Domination Set in a graph G is Dynamical k-total Domination Number of G. In this dissertation we first examine the most important results about Total Domination Number. Afterwards, we briefly comment on concept of k-Total Domination Number.In the end, we will introduce the new concept of Dynamical k-Total Domination. We examine the properties of the vertices member of a dynamical k-total domination set.we present upper bounds for dynamical k-total domination number in some graph families and compare deynamical k-total domination sets with k-total domination sets for same properties
  9. Keywords:
  10. Domination Number ; Hypergraph ; Claw-Free Graph

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