About Automorphisms of Graphs With Intersection Arrays {"44" ,"40" ,"12" ;"1,5" ,"33" } and {"48" ,"35,9" ;"1,7" ,"40" }
- Authors: Chen M.1, Makhnev A.A.2, Klimin V.S.3
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Affiliations:
- Hainan University
- Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
- Ural Federal University
- Issue: No 2 (65) (2024)
- Pages: 26-33
- Section: Mathematics
- URL: https://ogarev-online.ru/1993-0550/article/view/307273
- DOI: https://doi.org/10.17072/1993-0550-2024-2-26-33
- ID: 307273
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Abstract
Distance-regular graph Γ of diameter 3 with strongly regular graphs Γ2 and Γ3 has intersection array {r(c2+1)+a3, r c2, a3 + 1; 1, c2, r(c2 + 1)} (M.S. Nirova). For distance-regular graph Γ of diameter 3 and degree 44 there are exactly 7 feasible intersection arrays. For each of them graph Γ3 is strongly regular. For intersection array {44, 30, 5; 1, 3, 40} we have a3 = 4, c2 = 3, r = 10, Γ2 has parameters (540,440,358,360) and Γ3 has parameters (540,55,10,5). Graph does not exist (Koolen-Park). For intersection array {44, 35, 3; 1, 5, 42} graph Γ3 has parameters (375,22,5,1) and does not exist (its neighbourhood of vertex is the union of isolated 6-cliques). In this paper it is found futomorphisms of graphs with intersection arrays {44,40,12; 1,5,33 and 48,35,9; 1,7,40}.
About the authors
M. Chen
Hainan University
Author for correspondence.
Email: mzchen@hainanu.edu.cn
Candidate of Sciences (physical and mathematical), associate professor Haikou, China
A. A. Makhnev
Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Email: makhnev@imm.uran.ru
Doctor of Sciences (physical and mathematical), Professor, Corresponding Member of the Russian Academy of Sciences, Chief Researcher 620990, Russia, Yekaterinburg, 16 S. Kovalevskaya St.
V. S. Klimin
Ural Federal University
Email: kliminvasily@yandex.ru
postgraduate student 620075, Russia, Yekaterinburg, 51 Lenina Ave.
References
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- Makhnev, A.A., Bitkina, V.V. and Gutnova A.K. (2020), "Automorphisms of a distance regular graph with intersection array {48,35,9; 1,7,40}", Vladikavkaz. Mat. Zh., vol. 22, no. 2, pp. 24–33.
- Gavrilyuk, A. L. and Makhnev, A. A. (2010), "On Automorphisms of Distance-Regular Graphs with Intersection Array {56, 45, 1; 1, 9, 56}", Doklady Mathematics, vol. 432, no. 5, pp. 583-587.
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