# zbMATH — the first resource for mathematics

A classification of cubic symmetric graphs of order $$16p^2$$. (English) Zbl 1268.05102
Summary: A graph is called symmetric if its automorphism group acts transitively on its arc set. In this paper, we classify all connected cubic symmetric graphs of order $$16p^2$$ for each prime $$p$$.
##### MSC:
 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures 20F05 Generators, relations, and presentations of groups
##### Keywords:
regular coverings; symmetric graphs; invariant subspaces
Full Text:
##### References:
 [1] Conder M, Trivalent (cubic) symmetric graphs on up to 2048 vertices, http://www.math.auckland.ac.nz/conder/ (2006) [2] Conder M and Dobcsányi P, Trivalent symmetric graphs on up to 768 vertices, J. Combin. Math. Combin. Comput. 40 (2002) 41–63 · Zbl 0996.05069 [3] Du S F, Feng Y-Q, Kwak J H and Xu M Y, Cubic Cayley graphs on dihedral groups, Mathematical Analysis and Applications (New Delhi: Narosa Publishing House) (2004) pp. 224–235 [4] Feng Y Q, Kwak J H and Wang K, Classifying cubic symmetric graphs of order 8p or 8p 2, European J. Combin. 26 (2005) 1033–1052 · Zbl 1071.05043 · doi:10.1016/j.ejc.2004.06.015 [5] Feng Y Q, Kwak J H and Xu M Y, Cubic s-regular graphs of order 2p 3, J. Graph Theory 52 (2006) 341–352 · Zbl 1100.05073 · doi:10.1002/jgt.20169 [6] Feng Y Q and Kwak J H, Classifying cubic symmetric graphs of order 10p or 10p 2, Science in China A49(3) (2006) 300–319 · Zbl 1109.05051 · doi:10.1007/s11425-006-0300-9 [7] Feng Y Q and Kwak J H, Cubic symmetric graphs of order twice an odd prime-power, J. Austral. Math. Soc. 81 (2006) 153–164 · Zbl 1108.05050 · doi:10.1017/S1446788700015792 [8] Feng Y Q and Kwak J H, Cubic symmetric graphs of order a small number times a prime or a prime square, J. Combin Theory B97 (2007) 627–646 · Zbl 1118.05043 · doi:10.1016/j.jctb.2006.11.001 [9] Feng Y Q and Wang K, s-Regular cyclic coverins of the three-dimensional hypercube Q 3, European J. Combin. 24 (2003) 719–731 · Zbl 1035.05048 · doi:10.1016/S0195-6698(03)00055-6 [10] Gorenstein D, Finite Simple Groups (New York: Plenum Press) (1982) [11] Gross J L and Tucker T W, Generating all graph covering by permutation voltages assignment, Discrete Math. 18 (1977) 273–283 · Zbl 0375.55001 · doi:10.1016/0012-365X(77)90131-5 [12] Lorimer P, Vertex-transitive graphs: Symmetric graphs of prime valency, J. Graph Theory 8 (1984) 55–68 · Zbl 0535.05031 · doi:10.1002/jgt.3190080107 [13] Malnič A, Marušič D, Miklavič S and Potočnik P, Semisymmetric elementary abelian covers of the Mobius-Kantor graph, Discrete Math. 307 (2007) 2156–2175 · Zbl 1136.05026 · doi:10.1016/j.disc.2006.10.008 [14] Malnič A, Marušič D and Potočnik P, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 71–97 · Zbl 1065.05050 · doi:10.1023/B:JACO.0000047294.42633.25 [15] Oh J M, A classification of cubic s-regular graphs of order 14p, Discrete Math. 309(9) (2009) 2721–2726 · Zbl 1208.05055 · doi:10.1016/j.disc.2008.06.025 [16] Oh J M, A classification of cubic s-regular graphs of order 16p, Discrete Math. 309(10) (2009) 3150–3155 · Zbl 1177.05052 · doi:10.1016/j.disc.2008.09.001 [17] Sabidussi G, On a class of fixed-point-free graphs, Proc. Amer. Math. Soc. 9 (1958) 800–804 · Zbl 0091.37701 · doi:10.1090/S0002-9939-1958-0097068-7 [18] Suzuki M, Group Theory I (New York: Springer) (1982) [19] Tutte W T, A family of cubical graphs, Proc. Cambridge Philos. Soc. 43 (1947) 459–574 · Zbl 0029.42401 · doi:10.1017/S0305004100023720 [20] Wieldant H, Finite Permutation Groups (New York: Academic Press) (1964) [21] Xu M Y, Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math. 182 (1998) 309–319 · Zbl 0887.05025 · doi:10.1016/S0012-365X(97)00152-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.