A note on distance-regular graphs with a small number of vertices compared to the valency
SCIE
SCOPUS
- Title
- A note on distance-regular graphs with a small number of vertices compared to the valency
- Authors
- Koolen, JH; Park, J
- Date Issued
- 2013-08
- Publisher
- ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
- Abstract
- In this note we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given alpha > 2, there are finitely many distance-regular graphs Gamma with valency k, diameter D >= 3 and v vertices satisfying v < alpha k unless (D = 3 and Gamma is imprimitive) or (D = 4 and Gamma is antipodal and bipartite). We also show, as a consequence of this result, that there are finitely many distance-regular graphs with valency k >= 3, diameter D >= 3 and C-2 >= epsilon k for a given 0 < epsilon < 1 unless (D = 3 and Gamma is imprimitive) or (D = 4 and Gamma is antipodal and bipartite). Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.
- Keywords
- DIAMETER
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/14311
- DOI
- 10.1016/J.EJC.2013.01.006
- ISSN
- 0195-6698
- Article Type
- Article
- Citation
- EUROPEAN JOURNAL OF COMBINATORICS, vol. 34, no. 6, page. 935 - 940, 2013-08
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