Normal edge-transitive and 12−arc−transitive Cayley graphs on non-abelian groups of order 2pq, p>q are odd primes
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Darafsheh and Assari in [Normal edge-transitive Cayley graphs on non-abelian groups of order 4p, where p is a prime number, Sci. China Math., 56 (1) (2013) 213-219.] classified the connected normal edge transitive and 12−arc-transitive Cayley graph of groups of order 4p. In this paper we continue this work by classifying the connected Cayley graph of groups of order 2pq, p>q are primes. As a consequence it is proved that Cay(G,S) is a 12−arc-transitive Cayley graph of order 2pq, p>q if and only if |S| is an even integer greater than 2, S = T cup T^{-1} and T subseteq { cb^ja^{i} | 0 leq i leq p - 1}, 1 leq j leq q-1, such that T and T^{-1} are orbits of Aut(G,S) and begin{eqnarray*} G &cong& langle a, b, c | a^p = b^q = c^2 = e, ac = ca, bc = cb, b^{-1}ab = a^r rangle, or G &cong& langle a, b, c | a^p = b^q = c^2 = e, c ac = a^{-1}, bc = cb, b^{-1}ab = a^r rangle, end{eqnarray*} where r^q equiv 1 (mod p).
کلید واژگان
Cayley graphnormal edge-transitive
normal arc-transitive
05B25 Finite geometries
20D60 Arithmetic and combinatorial problems
شماره نشریه
3تاریخ نشر
2016-09-011395-06-11
ناشر
University of Isfahanسازمان پدید آورنده
University of KashanUniversity of Kashan
شاپا
2251-76502251-7669
