On tight distance-regular graphs
This thesis is an expository work taken from Sections 1-8 of the paper entitled Tight Distance-Regular Graphs by Aleksandar Jurisic, Jack Koolen, and Paul Terwilliger which will appear in the Journal of Algebraic Combinatorics. It focuses on the following result: Let T = (X, R) be a distance-regular...
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| Format: | text |
| Language: | English |
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Animo Repository
2000
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/2502 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/9340/viewcontent/TG03114_F_Partial.pdf |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | This thesis is an expository work taken from Sections 1-8 of the paper entitled Tight Distance-Regular Graphs by Aleksandar Jurisic, Jack Koolen, and Paul Terwilliger which will appear in the Journal of Algebraic Combinatorics. It focuses on the following result: Let T = (X, R) be a distance-regular graph with diameter d greater than or equal to 3 and eigenvalues k = Oo greater than O1 greater than ... greater than Od. Then the valency k, intersection numbers a1 and b1 satisfy (O1 + k over a1 + 1) (Od + k over a1 + 1) greater than or equal to -ka1b1 over (a1 + 1)2 T is said to be tight whenever T is nonbipartite, and the equality above holds. It also discusses characterizations of tight distance-regular graphs which involve intersection numbers and cosine sequences. |
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