normal edge-transitive and $frac{1}{2}-$arc$-$transitive cayley graphs on non-abelian groups of order $2pq$, $p > q$ are odd primes
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abstract
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 $frac{1}{2}-$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 begin{eqnarray*} g ≅& langle a, b, c | a^p = b^q = c^2 = e, ac = ca, bc = cb, b^{-1}ab = a^r rangle, or g ≅& 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 $r^q equiv 1 (mod p)$.
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normal edge-transitive and $ frac{1}{2}$-arc-transitive cayley graphs on non-abelian groups of order $2pq$ , $p > q$ are primes
darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (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 theconnected cayley graph of groups of order $2pq$, $p > q...
full textNormal edge-transitive Cayley graphs on the non-abelian groups of order $4p^2$, where $p$ is a prime number
In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.
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For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
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A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
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for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.
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Journal title:
international journal of group theoryجلد ۵، شماره ۳، صفحات ۱-۸
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