Let 1 be a distance-regular graph of diameter d and valency k>2. If b t =1 and 2t d, then 1 is an antipodal double-cover. Consequently, if f >2 is the multiplicity of an eigenvalue of the adjacency matrix of 1 and if 1 is not an antipodal doublecover then d 2f&3. This result is an improvement of God
Distance-regular Graphs with b2=1 and Antipodal Covers
✍ Scribed by Makoto Araya; Akira Hiraki; Aleksandar Jurisić
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 234 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
We show that a distance-regular graph of valency k Ͼ 2 is antipodal , if b 2 ϭ 1 . This answers Problem (i) on p . 182 of Brouwer , Cohen and Neumaier [4] .
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