NORMAL EDGE-TRANSITIVE AND ۱/۲−ARC−TRANSITIVE CAYLEY GRAPHS ON NON-ABELIAN GROUPS OF ORDER ۲pq, p > q ARE ODD PRIMES

چکیده مقاله

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 1 2−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 1 2−arc-transitive Cayley graph of order 2pq, p > q if and only if |S| is an even integer greater than 2, S = T ∪ T −1 and T ⊆ {cbj a i | 0 ≤ i ≤ p − 1}, 1 ≤ j ≤ q − 1, such that T and T −1 are orbits of Aut(G, S) and G ∼= ⟨a, b, c | a p = b q = c 2 = e, ac = ca, bc = cb, b−1 ab = a r ⟩, or G ∼= ⟨a, b, c | a p = b q = c 2 = e, cac = a −1 , bc = cb, b−1 ab = a r ⟩, where r q ≡ 1 (modp).