About Automorphisms of Graphs With Intersection Arrays {"44" ,"40" ,"12" ;"1,5" ,"33" } and {"48" ,"35,9" ;"1,7" ,"40" }
- 作者: Chen M.1, Makhnev A.A.2, Klimin V.S.3
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隶属关系:
- Hainan University
- Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
- Ural Federal University
- 期: 编号 2 (65) (2024)
- 页面: 26-33
- 栏目: Mathematics
- URL: https://journal-vniispk.ru/1993-0550/article/view/307273
- DOI: https://doi.org/10.17072/1993-0550-2024-2-26-33
- ID: 307273
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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}.
作者简介
M. Chen
Hainan University
编辑信件的主要联系方式.
Email: mzchen@hainanu.edu.cn
Candidate of Sciences (physical and mathematical), associate professor Haikou, China
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. Klimin
Ural Federal University
Email: kliminvasily@yandex.ru
postgraduate student 620075, Russia, Yekaterinburg, 51 Lenina Ave.
参考
- Brouwer, A.E., Cohen, A.M. and Neumaier A. (1989), Distance-Regular Graphs, Springer-Verlag, Berlin, Heidelberg New York.
- Chen, Minzhu, Makhnev, A.A. and Klimin V.S., "On distance-regular graphs of diameter 3 and degree 44".
- 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.
- Cameron, P.J. (1999), Permutation Groups, London Math. Soc. Student Texts № 45, Cambridge, Cambridge Univ. Press.
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