On distance-regular graphs with ki=kj, II
The thesis is an exposition of the article of A. Hiraki, H. Suzuki and M. Wajima entitled On Distance-Regular Graphs with ki = kj, II which is an improvement of H. Suzuki's paper. Major results such as the alternative proof of Terwilliger's inequality for bipartite distance-regular graphs...
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| Format: | text |
| Language: | English |
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Animo Repository
1997
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/1817 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8655/viewcontent/TG02631_F_Partial.pdf |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | The thesis is an exposition of the article of A. Hiraki, H. Suzuki and M. Wajima entitled On Distance-Regular Graphs with ki = kj, II which is an improvement of H. Suzuki's paper. Major results such as the alternative proof of Terwilliger's inequality for bipartite distance-regular graphs and the refinement of Ivanov's diameter bound are worked out in a more comprehensible mathematical language. Moreover, assume that T is a distance-regular graph of diameter d and i-th valency ki, where ki is the number of points at distance i from a vertex u in T. In addition, T satisfies ki = kj with i + j less than or equal to d. This study establishes the detailed proofs that T is a polygon (K=2) or an antipodal 2-cover (kd=1) by pressing definitions, lemmas and propositions with their corresponding examples and proofs. |
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