فهرست نشریات علمی دسترسی آزاد ایران

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 (2013) 213--219.] classified the connected normal edge transitive and $\frac{1}{2}-$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 $\frac{1}{2}-$arc-transitive Cayley graph of order $2pq$, $p > q$ if and only if $|S|$ is an even integer greater than 2, $S = T \cup T^{-1}$ 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$G ≅ < a, b, c  |  a^p = b^q = c^2 = e, ac = ca, bc = cb, b^{-1}ab = a^r >$,  or$G ≅ < a, b, c  |  a^p = b^q = c^2 = e, c ac = a^{-1}, bc = cb, b^{-1}ab = a^r >$,where $r^q \equiv 1  (mod p)$.