Tetravalent Arc-Transitive Graphs of Order 3p 2

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1. [1] Y.G. Baik, Y.-Q. Feng, H.S. Sim and M.Y. Xu, On the normality of Cayley graphs of abelian groups, Algebra Colloq. 5 (1998) 297-304. Zbl0904.05037
2. [2] N. Biggs, Algebraic Graph Theory, Second Ed. (Cambridge University Press, Cam- bridge, 1993). Zbl0284.05101
3. [3] W. Bosma, C. Cannon and C. Playoust, The MAGMA algebra system I: the user language, J. Symbolic Comput. 24 (1997) 235-265. doi:10.1006/jsco.1996.0125[Crossref] Zbl0898.68039
4. [4] C.Y. Chao, On the classification of symmetric graphs with a prime number of ver- tices, Trans. Amer. Math. Soc. 158 (1971) 247-256. doi:10.1090/S0002-9947-1971-0279000-7[Crossref] 
5. [5] Y. Cheng and J. Oxley, On weakly symmetric graphs of order twice a prime, J. Combin. Theory (B) 42 (1987) 196-211. doi:10.1016/0095-8956(87)90040-2[Crossref] Zbl0583.05032
6. [6] M. Conder, Orders of symmetric cubic graphs, The Second Internetional Workshop on Group Theory and Algebraic Combinatorics, (Peking University, Beijing, 2008). 
7. [7] M. Conder and C.E. Praeger, Remarks on path-transitivity on finite graphs, Euro- pean J. Combin. 17 (1996) 371-378. doi:10.1006/eujc.1996.0030[Crossref] Zbl0871.05029
8. [8] D.Ž. Djoković and G.L. Miller, Regular groups of automorphisms of cubic graphs, J. Combin. Theory (B) 29 (1980) 195-230. doi:10.1016/0095-8956(80)90081-7[Crossref] 
9. [9] Y.-Q. Feng and J.H. Kwak, One-regular cubic graphs of order a small number times a prime or a prime square, J. Aust. Math. Soc. 76 (2004) 345-356. doi:10.1017/S1446788700009903[Crossref] Zbl1055.05078
10. [10] Y.-Q. Feng and J.H. Kwak, Classifying cubic symmetric graphs of order 10p or 10p2, Sci. China (A) 49 (2006) 300-319. doi:10.1007/s11425-006-0300-9[Crossref] Zbl1109.05051
11. [11] Y.-Q. Feng and J.H. Kwak, Cubic symmetric graphs of order twice an odd prime power, J. Aust. Math. Soc. 81 (2006) 153-164. doi:10.1017/S1446788700015792[Crossref] 
12. [12] Y.-Q. Feng and J.H. Kwak, Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin. Theory (B) 97 (2007) 627-646. doi:10.1016/j.jctb.2006.11.001[Crossref] Zbl1118.05043
13. [13] Y.-Q. Feng, J.H. Kwak and K.S. Wang, Classifying cubic symmetric graphs of order 8p or 8p2, European J. Combin. 26 (2005) 1033-1052. doi:10.1016/j.ejc.2004.06.015[Crossref] Zbl1071.05043
14. [14] R. Frucht, A one-regular graph of degree three, Canad. J. Math. 4 (1952) 240-247. doi:10.4153/CJM-1952-022-9[Crossref] Zbl0046.40903
15. [15] A. Gardiner and C.E. Praeger, On 4-valent symmetric graphs, European. J. Combin. 15 (1994) 375-381. doi:10.1006/eujc.1994.1041[Crossref] Zbl0806.05037
16. [16] A. Gardiner and C.E. Praeger, A characterization of certain families of 4-valent symmetric graphs, European. J. Combin. 15 (1994) 383-397. doi:10.1006/eujc.1994.1042 Zbl0806.05038
17. [17] M. Ghasemi, A classification of tetravalent one-regular graphs of order 3p2, Colloq. Math. 128 (2012) 15-24. doi:10.4064/cm128-1-3[Crossref][WoS] Zbl1258.05048
18. [18] M. Ghasemi and J.-X. Zhou, Tetravalent s-transitive graphs of order 4p2, Graphs Combin. 29 (2013) 87-97. doi:10.007/s00373-011-1093-3 Zbl1258.05049
19. [19] D. Gorenstein, Finite Simple Groups (Plenum Press, New York, 1982). doi:10.1007/978-1-4684-8497-7[Crossref] Zbl0483.20008
20. [20] C.H. Li, Finite s-arc-transitive graphs, The Second Internetional Workshop on Group Theory and Algebraic Combinatorics, (Peking University, Beijing, 2008). 
21. [21] C.H. Li, The finite vertex-primitive and vertex-biprimitive s-transitive graphs for s ≥ 4, Trans. Amer. Math. Soc. 353 (2001) 3511-3529. doi:10.1090/S0002-9947-01-02768-4[Crossref] Zbl0974.05042
22. [22] C.H. Li, Z.P. Lu and D. Maruˇsiˇc, On primitive permutation groups with small sub- orbits and their orbital graphs, J. Algebra 279 (2004) 749-770. doi:10.1016/j.jalgebra.2004.03.005[Crossref] 
23. [23] C.H. Li, Z.P. Lu and H. Zhang, Tetravalent edge-transitive Cayley graphs with odd number of vertices, J. Combin. Theory (B) 96 (2006) 164-181. doi:10.1016/j.jctb.2005.07.003[Crossref] Zbl1078.05039
24. [24] R.C. Miller, The trivalent symmetric graphs of girth at most six, J. Combin. Theory (B) 10 (1971) 163-182. doi:10.1016/0095-8956(71)90075-X[Crossref] 
25. [25] P. Potoˇcnik, P. Spiga and G. Verret. http://www.matapp.unimib.it/spiga/ 
26. [26] P. Potoˇcnik, P. Spiga and G. Verret, Cubic vertex-transitive graphs on up to 1280 vertices. arXiv:1201.5317v1 [math.CO]. Zbl1256.05102
27. [27] C.E. Praeger, An O’Nan-Scott theorem for finite quasiprimitive permutation groups and an application to 2-arc transitive graphs, J. London Math. Soc. 47 (1993) 227-239. doi:10.1112/jlms/s2-47.2.227[Crossref] 
28. [28] D.J.S. Robinson, A Course in the Theory of Groups (Springer-Verlag, New York, 1982). Zbl0483.20001
29. [29] W.T. Tutte, A family of cubical graphs, Proc. Camb. Phil. Soc. 43 (1947) 459-474. doi:10.1017/S0305004100023720[Crossref] Zbl0029.42401
30. [30] R.J. Wang and M.Y. Xu, A classification of symmetric graphs of order 3p, J. Com- bin. Theory (B) 58 (1993) 197-216. doi:10.1006/jctb.1993.1037[Crossref] Zbl0793.05074
31. [31] R. Weiss, The nonexistence of 8-transitive graphs, Combinatorica 1 (1981) 309-311. doi:10.1007/BF02579337[Crossref] Zbl0486.05032
32. [32] S. Wilson and P. Potoˇcnik, A Census of edge-transitive tetravalent graphs. http://jan. ucc.nau.edu/swilson/C4Site/index.html. 
33. [33] M.Y. Xu, A note on one-regular graphs, Chinese Sci. Bull. 45 (2000) 2160-2162. 
34. [34] J. Xu and M.Y. Xu, Arc-transitive Cayley graphs of valency at most four on abelian groups, Southeast Asian Bull. Math. 25 (2001) 355-363. doi:10.1007/s10012-001-0355-z [Crossref] Zbl0993.05086
35. [35] J.-X. Zhou, Tetravalent s-transitive graphs of order 4p, Discrete Math. 309 (2009) 6081-6086. doi:10.1016/j.disc.2009.05.014[Crossref][WoS] 
36. [36] J.-X. Zhou and Y.-Q. Feng, Tetravalent s-transitive graphs of order twice a prime power, J. Aust. Math. Soc. 88 (2010) 277-288. doi:10.1017/S1446788710000066 [Crossref]