DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST
In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are \(\{18,14,5;1,2,14\}\), \(\{18,15,9;1,1,10\}\), \(\{21,16,10;1,2,12\}\), \(\{24,21,3;1,3,18\}\), and \(\{27,20,7;1,4,21\}\). Automorphi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2020-12-01
|
| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/292 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849410941593059328 |
|---|---|
| author | Konstantin S. Efimov Alexander A. Makhnev |
| author_facet | Konstantin S. Efimov Alexander A. Makhnev |
| author_sort | Konstantin S. Efimov |
| collection | DOAJ |
| description | In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are \(\{18,14,5;1,2,14\}\), \(\{18,15,9;1,1,10\}\), \(\{21,16,10;1,2,12\}\), \(\{24,21,3;1,3,18\}\), and \(\{27,20,7;1,4,21\}\). Automorphisms of graphs with intersection arrays \(\{18,15,9;1,1,10\}\) and \(\{24,21,3;1,3,18\}\) were found earlier by A.A. Makhnev and D.V. Paduchikh. In this paper, it is proved that a graph with the intersection array \(\{27,20,7;1,4,21\}\) does not exist. |
| format | Article |
| id | doaj-art-8948280c5cc2427a8f2e9909ac42b06b |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2020-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-8948280c5cc2427a8f2e9909ac42b06b2025-08-20T03:34:56ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522020-12-016210.15826/umj.2020.2.006111DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXISTKonstantin S. Efimov0Alexander A. Makhnev1Ural State University of Economics, 62 March 8th Str., Ekaterinburg, 620144; Ural Federal University, 19 Mira Str., Ekaterinburg, 620002Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620108; Ural Federal University, 19 Mira Str., Ekaterinburg, 620002, RussiaIn the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are \(\{18,14,5;1,2,14\}\), \(\{18,15,9;1,1,10\}\), \(\{21,16,10;1,2,12\}\), \(\{24,21,3;1,3,18\}\), and \(\{27,20,7;1,4,21\}\). Automorphisms of graphs with intersection arrays \(\{18,15,9;1,1,10\}\) and \(\{24,21,3;1,3,18\}\) were found earlier by A.A. Makhnev and D.V. Paduchikh. In this paper, it is proved that a graph with the intersection array \(\{27,20,7;1,4,21\}\) does not exist.https://umjuran.ru/index.php/umj/article/view/292distance-regular graph, graph \(\gamma\) with strongly regular graph \(\gamma_3\), automorphism |
| spellingShingle | Konstantin S. Efimov Alexander A. Makhnev DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST Ural Mathematical Journal distance-regular graph, graph \(\gamma\) with strongly regular graph \(\gamma_3\), automorphism |
| title | DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST |
| title_full | DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST |
| title_fullStr | DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST |
| title_full_unstemmed | DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST |
| title_short | DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST |
| title_sort | distance regular graph with intersection array 27 20 7 1 4 21 does not exist |
| topic | distance-regular graph, graph \(\gamma\) with strongly regular graph \(\gamma_3\), automorphism |
| url | https://umjuran.ru/index.php/umj/article/view/292 |
| work_keys_str_mv | AT konstantinsefimov distanceregulargraphwithintersectionarray272071421doesnotexist AT alexanderamakhnev distanceregulargraphwithintersectionarray272071421doesnotexist |