On Automorphisms of a Distance-Regular Graph with Intersection Array {125, 96, 1; 1, 48, 125}
- Authors: Bitkina V.V.1, Makhnev A.A.2
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Affiliations:
- Khetagurov North Ossetian State University
- Krasovskii Institute of Mathematics and Mechanics, Ural Branch
- Issue: Vol 39, No 3 (2018)
- Pages: 458-463
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201939
- DOI: https://doi.org/10.1134/S1995080218030058
- ID: 201939
Cite item
Abstract
J. Koolen posed the problem of studying distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs whose second eigenvalue is at most t for a given positive integer t. This problem is reduced to the description of distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with a nonprincipal eigenvalue t for t = 1, 2,.... In the paper “Distance regular graphs in which local subgraphs are strongly regular graphs with the second eigenvalue at most 3”, Makhnev and Paduchikh found intersection arrays of distance-regular graphs in which the neighborhoods of vertices are strongly regular graphs with second eigenvalue t, where 2 < t ≤ 3. Graphs with intersection arrays {125, 96, 1; 1, 48, 125}, {176, 150, 1; 1, 25, 176}, and {256, 204, 1; 1, 51, 256} remained unexplored. In this paper, possible orders and fixed-point subgraphs of automorphisms are found for a distance-regular graph with intersection array {125, 96, 1; 1, 48, 125}. It is proved that the neighborhoods of the vertices of this graph are pseudogeometric graphs for GQ(4, 6). Composition factors of the automorphism group for a distance-regular graph with intersection array {125, 96, 1; 1, 48, 125} are determined.
About the authors
V. V. Bitkina
Khetagurov North Ossetian State University
Author for correspondence.
Email: bviktoriyav@mail.ru
Russian Federation, Vladikavkaz, 362025
A. A. Makhnev
Krasovskii Institute of Mathematics and Mechanics, Ural Branch
Email: bviktoriyav@mail.ru
Russian Federation, Yekaterinburg, 620990