About Automorphisms of Graphs With Intersection Arrays {44,40,12; 1,5,33} and {48,35,9; 1,7,40}
DOI:
https://doi.org/10.17072/1993-0550-2024-2-26-33Keywords:
distance-regular graph, strongly regular graph, intersection arrayAbstract
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}.References
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Copyright (c) 2024 Минчжу Чень, Александр Алексеевич Махнев, Василий Семенович Климин
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