On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125}
J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue ≤ t for the given positive integer t. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices ar...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2017-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | http://kpfu.ru/portal/docs/F1711774893/159_1_phys_mat_2.pdf |
| _version_ | 1826952282005045248 |
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| author | V.V. Bitkina A.A. Makhnev |
| author_facet | V.V. Bitkina A.A. Makhnev |
| author_sort | V.V. Bitkina |
| collection | DOAJ |
| description | J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue ≤ t for the given positive integer t. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the non-principal 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”, A.A. Makhnev and D.V. Paduchikh found the arrays of intersections of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue t such as 2 < t ≤ 3. The graphs with intersection arrays {125,96,1;1,48,125}, {176,150,1;1,25,176}, and {256,204,1;1,51,256} remain unexplored.
In this paper, we have found the possible orders and the structures of subgraphs of the fixed points of automorphisms of a distance-regular graph with the intersection array {125,96,1;1,48,125}. It has been proved that the neighborhoods of the vertices of this graph are pseudogeometric graphs for GQ(4,6). Composition factors of the automorphism group of a distance-regular graph with the intersection array {125,96,1;1,48,125} have been determined. |
| first_indexed | 2024-04-11T03:39:23Z |
| format | Article |
| id | doaj.art-eb5bf0df471249038f55634e59fd05f6 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2025-02-17T23:04:40Z |
| publishDate | 2017-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj.art-eb5bf0df471249038f55634e59fd05f62024-12-02T09:09:33ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982017-03-0115911320On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125}V.V. Bitkina0A.A. Makhnev1North Ossetian State University, Vladikavkaz, 362025 RussiaInstitute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990 RussiaJ. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue ≤ t for the given positive integer t. This problem is reduced to the description of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the non-principal 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”, A.A. Makhnev and D.V. Paduchikh found the arrays of intersections of distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue t such as 2 < t ≤ 3. The graphs with intersection arrays {125,96,1;1,48,125}, {176,150,1;1,25,176}, and {256,204,1;1,51,256} remain unexplored. In this paper, we have found the possible orders and the structures of subgraphs of the fixed points of automorphisms of a distance-regular graph with the intersection array {125,96,1;1,48,125}. It has been proved that the neighborhoods of the vertices of this graph are pseudogeometric graphs for GQ(4,6). Composition factors of the automorphism group of a distance-regular graph with the intersection array {125,96,1;1,48,125} have been determined.http://kpfu.ru/portal/docs/F1711774893/159_1_phys_mat_2.pdfdistance-regular graphautomorphism groups of graph |
| spellingShingle | V.V. Bitkina A.A. Makhnev On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} Учёные записки Казанского университета: Серия Физико-математические науки distance-regular graph automorphism groups of graph |
| title | On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} |
| title_full | On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} |
| title_fullStr | On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} |
| title_full_unstemmed | On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} |
| title_short | On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} |
| title_sort | on automorphisms of a distance regular graph with intersection array 125 96 1 1 48 125 |
| topic | distance-regular graph automorphism groups of graph |
| url | http://kpfu.ru/portal/docs/F1711774893/159_1_phys_mat_2.pdf |
| work_keys_str_mv | AT vvbitkina onautomorphismsofadistanceregulargraphwithintersectionarray125961148125 AT aamakhnev onautomorphismsofadistanceregulargraphwithintersectionarray125961148125 |