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Generation, Propagation and Domination in Graphs

Mohammad Ali Tajrishi, Mahshid | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48868 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahmoodian, Ebadollah; Tusserkani, Roozbeh
  7. Abstract:
  8. In this thesis, we discuss some basic concepts of graph theory and introduce some well-known graphs with a glimpse at the optimization concepts. We also have discussed the proof of theorems related with the domination sets and total domination sets. Indeed, let G = (V;E) be a graph with no isolated vertex. A subset of V , S is a domination set if every vertex in V n S is adjacent to at least one vertex in S. Also, a subset of V , S is a total domination set if every vertex in V is adjacent to at least one vertex in S. Generation and propagation codes that is introduced by R.Touserkani is one of the objects in this thesis, that we study and discuss. Also, for some classes of graphs, we examine generation and propagation codes. Then we introduce a new concept called k-supported domination and provide an overview of it and focus specifically on k = 2. The concept of k-supported domination is defined on a graph G = (V;E) with no isolated vertex, a subset of V , such that S is a domination set and we have (G[S]) k. Finally, we discuss some examples and theorems of some specific family of graphs for 2-supported domination sets, also introduce some conjectures on the subject
  9. Keywords:
  10. Domination ; Dominating Set ; Total Domination Set ; 2-Supported Domination ; k-Supported Domination ; Generation and Propagation Codes

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