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Normal edge-transitive and ½ -ARC-transitive cayley graphs on non-abelian groups of order 2pq, p > q are odd primes | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 5، شماره 3، آذر 2016، صفحه 1-8 اصل مقاله (206.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.6537 | ||
| نویسندگان | ||
| Ali Reza Ashrafi* ؛ Bijan Soleimani | ||
| University of Kashan | ||
| چکیده | ||
| 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 $r^q \equiv 1 (mod p)$. | ||
| کلیدواژهها | ||
| Cayley graph؛ normal edge-transitive؛ normal arc-transitive | ||
| مراجع | ||
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[1] N. Biggs, Algeraic Graph Theory, Cambridge University Press, Cambridge, 1974.
[2] M. R. Darafsheh and A. Assari, Normal edge-transitive Cayley graphs on non-ab elian groups of order 4 p, where p is a prime numb er, Sci. China Math., 56 (2013) 213-219.
[3] X. G. Fang, C. H. Li and M. Y. Xu, On edge-transitive Cayley graphs of valency four, European J. Combin., 25 (2004) 1107-1116.
[4] C. D. Go dsil, On the full automorphism group of a graph, Combinatorica, 1 (1981) 243-256.
[5] P. C. Houlis, Quotients of normal edge-transitive Cayley graphs, MSc Thesis, University of Western Australia, 1998.
[6] C. H. Li, Z. P. Lu and H. Zhang, Tetravalent edge-transitive Cayley graphs with o dd numb er of vertices, J. Combin. Theory Ser. B, 96 (2006) 164-181.
[7] C. E. Praeger, Finite normal edge-transitive Cayley graphs, Bul l. Austral. Math. Soc., 60 (1999) 207-220.
[8] A. A. Talebi, Some normal edge-transitive Cayley graphs on dihedral groups, J. Math. Comput. Sci., 2 (2011) 448-452.
[9] C. Q. Wang, D. J. Wang and M. Y. Xu, On normal Cayley graphs of nite groups, Sci. China Ser. A, 28 (1998) 131-139.
[10] M. Y. Xu, Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math. , 182 (1998) 309-319.
[11] C. Zhang, J.-X. Zhou and Y.-Q. Feng, Automoprphisms of cubic Cayley graphs of order 2p q, Discrete Math., 309 (2009) 2687-2695. | ||
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