On application of linear algebra in classification of symmetry elmentary abelian covers of the Narou graph

Document Type : Original Paper


Department of Mathematics, University of Mazandaran, Babolsar, Iran



Let 𝑋 be a graph and G ≤ 𝐴𝑢𝑡(𝑋). the graph 𝑋 is called 𝐺 -symmetric if 𝐺 acts transitively

on its arcs. The covering technique has long been known as a powerful tool in topology and

graph theory. In this paper, by using the concepts of linear algebra and covering techniques, we

will classify the symmetric elementary abelian covers of the Nauru graph for one of its

symmetric subgroups


Main Subjects

[1] R.A. Beezer, Sage for linear algebra; A supplement to a first course in linear algebra, Sage web site http://www.sagemath.org. 2011.
[2] W. Bosma and J. Cannon, Handbook of Magma Function, Sydney University Press, Sydney, 1994.
[3] Y. Cheng and J. Oxley, On weakly symmetric graphs of order twice a prime, J. Combin. Theory Ser. B 42 (1987), 196–211.
[4] M. Conder, Trivalent (cubic) symmetric graphs on up to 2048 vertices, http://www.math.auckland.ac.nz conder/symmcubic2048list.txt, J (2006).
[5] M. Conder and P. Dobcsanyi, Trivalent symmetric graphs on up to 768 vertices, J. Combin. Math. Combin. Comput. 40 (2002), 41–63.
[6] D.S. Dumit and R.M. Foote, Abstract algebra, 2003.
[7] Y.Q. Feng and J. H. Kwak, Classifying cubic symmetric graphs of order 10p or 10p2, Sci. China Ser. A 49 (2006), 300–319.
[8] Y.Q. Feng, J. H. Kwak and K. Wang, Classifying cubic symmetric graphs of order 8p or 8p2, European J. Combin. 26 (2005), 1033–1052.
[9] Y.Q. Feng, J.H. Kwak and M.Y. Xu, Cubic s-regular graphs of order 2p3, J. Graph Theory 52 (2006), 341–352.
[10] 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 94 (2007), 627–646.
[11] A. Gardiner and C.E. Praeger, On 4-valent symmetric graphs, European. J. Combin, 15 (1994), 375–381.
[12] A. Gardiner and C.E. Praeger, A characterization of certain families of 4-valent symmetric graphs, European. J. Combin, 15 (1994), 383–397.
[13] M. Ghasemi, A classification of tetravalent one-regular graphs of order 3p2, Colloq.Math, 128 (2012), 15–24.
[14] M. Ghasemi and J.X. Zhou, Tetravalent s-transitive graphs of order 4p2, Graphs Combin, 29 (2012), 87–97.
[15] J.L. Gross and T.W. Tucker, Generating all graph covering by permutation voltages assignment, Discrete Math. 18 (1977), 273–283.
[16] P.J. Hilton and S. Wylie, Homology theory, an introduction to algebraic topology, cambridge university, 1960.
[17] X.H. Hua, Y.Q. Feng and J. Lee, Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259–2267.
[18] J.H. Kwak and J.M. Oh, Arc transitive elementary abelian covers of the octahedron graph, Linear algebra and its applications, 429 (2008), 2180–2198.
[19] A. Malnič, Group actions, covering and lifts of automorphisms, Discrete Math. 182 (1998), 203–218.
[20] A. Malnič, D. Marusič, S. Miklavič and P. Potočnik, Semisymmetric elementary abelian covers of the Mobius-Kantor graph, Discrete Math. 307 (2007), 2156–2175.
[21] A. Malnič , D. Marusič and P. Potočnik , Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004), 71–97.
[22] A. Malnič and P. Potočnik, Invariant subspaces, duality, and covers of the Petersen graph, European J. Combin. 27 (2006), 971–989.
[23] W.S. Massey, Algebraic topology: an introduction, 1976.
[24] A.A. Talebi and N. Mehdipoor, Classifying cubic s-regular graphs of orders 22p, 22p2, Algebra Discrete Math. 16 (2013), 293–298.
[25] W.T. Tutte, Connectivity in graphs, Toronto University Press, 1966.