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An infinite family of cubic edge- but not vertex-transitive graphs |
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| Affiliation: | a IMFM, Oddelek za Matematiko, Univerza v Ljubljani, Jadranska 19, 1111 Ljubljana, Slovenia b Department of System Sciences and Mathematics, Zhengzhou University, Henan Province 450052, People's Republic of China |
| Abstract: | An infinite family of cubic edge- but not vertex-transitive graphs is constructed. The graphs are obtained as regular -covers of K3,3 where n=p1e1p2e2pkek where pi are distinct primes congruent to 1 modulo 3, and ei1. Moreover, it is proved that the Gray graph (of order 54) is the smallest cubic edge- but not vertex-transitive graph. |
| Keywords: | Author Keywords: Covering protection Lifting automorphisms Edge-transitive graph Semisymmetric graph Gray graph |
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