| نویسندگان | سید علیرضا اشرفی قمرودی-بیژن سلیمانی |
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| تاریخ انتشار | 2016-4-01 |
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| رتبه نشریه | علمی - پژوهشی |
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| نمایه نشریه | ISI ,ISC ,SID |
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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).
