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- W2026490023 abstract "In this paper, all pairwise non-isomorphic p -elementary abelian covering projections admitting a lift of an arc-transitive subgroup of the full automorphism group of the Pappus graph F 18 , the unique connected cubic symmetric graph of order 18, are constructed. The number of such covering projections is equal to 5, 19, 9, 11 and 5 if p = 2 , p = 3 , p ≡ 7 ( mod 12 ) , p ≡ 1 ( mod 12 ) and p ≡ 5 ( mod 6 ) , respectively. As results, three infinite families of cubic s -regular graphs for s = 1 , 2 and 3 are constructed, and a classification of the cubic s -regular graphs of order 18 p for each s ≥ 1 and each prime p is given. From the classification of cubic s -regular graphs of order 18 p we have the following: (1) apart from the two 5-regular graphs F 90 and F 234 B and the 2-regular graph F 54 , all of these graphs are 1-regular with p ≡ 1 ( mod 6 ) ; (2) apart from F 90 and F 234 B all of these graphs are of girth 6; (3) apart from F 234 B all of these graphs are bipartite." @default.
- W2026490023 created "2016-06-24" @default.
- W2026490023 creator A5045342880 @default.
- W2026490023 date "2009-12-01" @default.
- W2026490023 modified "2023-09-29" @default.
- W2026490023 title "Arc-transitive elementary abelian covers of the Pappus graph" @default.
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- W2026490023 doi "https://doi.org/10.1016/j.disc.2009.07.010" @default.
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