Distance-regular graphs with a relatively small eigenvalue multiplicity
SCIE
SCOPUS
- Title
- Distance-regular graphs with a relatively small eigenvalue multiplicity
- Authors
- Koolen, JH; Kim, J; Park, J
- Date Issued
- 2013-01-07
- Publisher
- ELECTRONIC JOURNAL OF COMBINATORICS
- Abstract
- Godsil showed that if Gamma is a distance-regular graph with diameter D >= 3 and valency k >= 3, and theta is an eigenvalue of Gamma with multiplicity m >= 2, then k <= (m+2)(m-1)/2. In this paper we will give a refined statement of this result. We show that if Gamma is a distance-regular graph with diameter D >= 3, valency k >= 2 and an eigenvalue theta with multiplicity m >= 2, such that k is close to (m+2)(m-1)/2, then theta must be a tail. We also characterize the distance-regular graphs with diameter D >= 3, valency k >= 3 and an eigenvalue theta with multiplicity m >= 2 satisfying k = (m+2)(m-1)/2.
- Keywords
- TAILS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15709
- DOI
- 10.37236/2410
- ISSN
- 1077-8926
- Article Type
- Article
- Citation
- ELECTRONIC JOURNAL OF COMBINATORICS, vol. 20, no. 1, 2013-01-07
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