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Valency of Distance-regular Antipodal Graphs with Diameter 4

✍ Scribed by Štefko Miklavič

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
141 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis

Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n -1)/2 holds. This result implies that only one of a complementary pair of strongly regular graphs can be the antipodal quotient of an antipodal distanceregular graph.

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