Mohsen SHAHSAVARAN, Mohammad Reza DARAFSHEH

Classifying semisymmetric cubic graphs of order 20p

A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. In thispaper we classify all connected cubic semisymmetric graphs of order 20p, p prime.

PDF

___

[1] Alaeiyan M, Ghasemi M. Cubic edge-transitive graphs of order 8p2 . Bulletin of the Australian Mathematical Society 2008; 77 (2): 315-323.
[2] Alaeiyan M, Onagh BN. On semisymmetric cubic graphs of order 10p3 . Hacettepe Journal of Mathematics and Statistics 2011; 40 (4): 531-535.
[3] Bugeand Y, Cao Z, Mignotte M. On simple K4 -groups. Journal of Algebra 2001; 241(2):658–668.
[4] Butler G, McKay J. The transitive groups of degree up to eleven. Communications in Algebra 1983; 11 (8): 863-911.
[5] Conder M, Malnič A, Marušič D, Potočnik P. A census of semisymmetric cubic graphs on up to 768 vertices. Journal of Algebraic Combinatorics 2006; 23 (3): 255-294.
[6] Conder M, Nedela R. A refined classification of symmetric cubic graphs. Journal of Algebra 2009; 322: 722-740.
[7] Du S, Xu M. A classification of semisymmetric graphs of order 2pq . Communications in Algebra 2000; 28 (6): 2685-2715.
[8] Feng Y, Ghasemi M, Changqun W. Cubic semisymmetric graphs of order 6p3 . Discrete Mathematics 2010; 310 (17): 2345-2355.
[9] Folkman J. Regular line-symmetric graphs. Journal of Combinatorial Theory 1967; 3 (3): 215-232.
[10] Goldschmidt DM. Automorphisms of trivalent graphs. Annals of Mathematics 1980; 111 (2): 377-406.
[11] Han H, Lu Z. Semisymmetric graphs of order 6p2 and prime valency. Science China Mathematics 2012; 55 (12): 2579-2592.
[12] Herzog M. On finite simple groups of order divisible by three primes only. Journal of Algebra 1968; 120 (10): 383-388.
[13] Hua X, Feng Y. Cubic semisymmetric graphs of order 8p3 . Science China Mathematics 2011; 54 (9): 1937-1949.
[14] Kwak JH, Nedela R. Graphs and Their Coverings. Lecture Notes Series Vol. 17. Bratislava, Slovakia: Slovak Academy of Sciences, 2007.
[15] Lu Z, Wang C, Xu M. On semisymmetric cubic graphs of order 6p2 . Science in China, Series A: Mathematics 2004; 47 (1): 1-17.
[16] Malnič A, Marušič D, Wang C. Cubic Semisymmetric Graphs of Order 2p3 . Ljubljana, Slovenia: University of Ljubljana Preprint Series, 2000.
[17] Malnič A, Marušič D, Wang C. Cubic edge-transitive graphs of order 2p3 . Discrete Mathematics 2004; 274 (1-3): 187-198.
[18] Robinson DJ. A Course in the Theory of Groups. New York, NY, USA: Springer-Verlag, 1982.
[19] Shi WJ. On simple K4 -groups. Chinese Science Bulletin 1991; 36 (17): 1281-1283.
[20] Suzuki M. Group Theory. New York, USA: Springer-Verlag, 1986.
[21] Talebi A, Mehdipoor N. Classifying cubic semisymmetric graphs of order 18pn . Graphs and Combinatorics 2014; 30 (4): 1037-1044.
[22] The GAP Group. Groups, Algorithms and Programming. Version 4.8.6, 2016; http://www.gap-system.org.
[23] Tutte WT. Connectivity in Graphs. Toronto, Canada: University of Toronto Press, 1966.
[24] Zhang S, Shi WJ. Revisiting the number of simple K4 -groups. arXiv: 1307.8079v1 [math.NT], 2013.