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Combinatorial Curvature of Graphs

Pournajafi, Pegah | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51423 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Daneshgar, Amir; Javadi Jourtani, Ramin
  7. Abstract:
  8. There are a variety of notions of curvature that one could define on graphs. In this thesis, we introduce one of them which is called the ”Combinatorial Curvature”. This curvature is defined on graphs embedded on a surface, however as the name suggests,the combinatorial curvature of a vertex depends only on the combinatorial properties of the graph, and not on the geometric properties of the surface on which the graph is embedded. More precisely, the combinatorial curvature of a vertex is a function of the degree of the vertex and the faces which are incident to that vertex.In the main part of this thesis, we have tried to collect the most important results about the combinatorial curvature. Also, we conclude the thesis by a concise discussion on the subject and listing some of the open problems in this area of research
  9. Keywords:
  10. Graph Theory ; Curvature ; Combinatorial Carvature ; Topological Graph Theory