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Distance-regular Graphs of the Heighth

✍ Scribed by Akira Hiraki


Book ID
106048043
Publisher
Springer Japan
Year
1999
Tongue
English
Weight
110 KB
Volume
15
Category
Article
ISSN
0911-0119

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Let Ξ“ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (Ξ») > n -1, then D ≀ d -1, where P is the polynomial of degree d-1 which takes alternating values Β±1 at Ξ» 1 , . . . , Ξ» d . The graphs satisfying P (Ξ») = n -1, called boundary graphs, h

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In [1] N.L. Biggs mentions two parameter sets for distance regular graphs that are antipodal covers of a complete graph, for which existence of a corresponding graph was unknown. Here we settle both cases by proving that one does not exist, while there are exactly two nonisomorphic solutions to the