Transitive distance-regular graphs from linear groups $L(3,q)$‎, ‎$q = 2,3,4,5

In this paper we classify distance-regular graphs‎, ‎including strongly regular graphs‎, ‎admitting a transitive action of the linear groups $L(3,2)$‎, ‎$L(3,3)$‎, ‎$L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15‎. ‎We give details about constructed graphs‎....

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Bibliographic Details
Published in:	Transactions on combinatorics Vol. 9; no. 1; pp. 49 - 60
Main Author:	Andrea Svob
Format:	Journal Article
Language:	English
Published:	University of Isfahan 01-03-2020
Subjects:	distance-regular graph linear group self-orthogonal code strongly regular graph
Online Access:	Get full text
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Summary:	In this paper we classify distance-regular graphs‎, ‎including strongly regular graphs‎, ‎admitting a transitive action of the linear groups $L(3,2)$‎, ‎$L(3,3)$‎, ‎$L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15‎. ‎We give details about constructed graphs‎. ‎In addition‎, ‎we construct self-orthogonal codes from distance-regular graphs obtained in this paper‎.
ISSN:	2251-8657 2251-8665
DOI:	10.22108/toc.2020.116255.1630