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Nonexistence of some Antipodal Distance-regular Graphs of Diameter Four

✍ Scribed by Aleksandar Jurišić; Jack Koolen

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
160 KB
Volume
21
Category
Article
ISSN
0195-6698

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✦ Synopsis

We find an inequality involving the eigenvalues of a regular graph; equality holds if and only if the graph is strongly regular. We apply this inequality to the first subconstituents of a distance-regular graph and obtain a simple proof of the fundamental bound for distance-regular graphs, discovered by Jurišić, Koolen and Terwilliger. Using this we show that for distance-regular graphs with certain intersection arrays, the first subconstituent graphs are strongly regular. From these results we prove the nonexistence of distance-regular graphs associated to 20 feasible intersection arrays from the book Distance-Regular Graphs by Brouwer, Cohen and Neumaier [3].

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