Normal edge-transitive Cayley graphs on the non-abelian groups of order $4p^2$, where $p$ is a prime number

Document Type : Research Paper


Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Tarbiat Modares University P.O‎. ‎Box 14115-137‎, ‎Tehran‎, ‎Iran.


In this paper, we determine all of connected normal edge-transitive Cayley graphs on non-abelian groups with order $4p^2$, where $p$ is a prime number.


Main Subjects

M. Alaeiyan, On normal edge-transitive Cayley graphs of some abelian groups, Southeast Asian Bull. Math. 33 (2009) 13--19.
M. Darafsheh and A. Assari, 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.
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.
C.D. Godsil, On the full automorphism group of a graph, Combinatorica 1 (1981) 243--256.
C.D. Godsil and G. Royle, Algebraic Graph Theory, New York: Springer, 2001.
P.C. Houlis, Quotients of normal edge-transitive Cayley graphs, MS Thesis, University of Western Australia, 1998.
C.H. Li, Z.P. Lu and H. Zhang, Tetravalent edge-transitive Cayley graphs with odd number of vertices, J. Combin. Theory Ser. B 96 (2006) 164--181.
J.E. Iiamas, On Difference Sets in Groups of Order 4p2, J. Combin. Theory Ser A 72 (1995) 256--276.
D. Marusic and R. Nedela, Maps and half-transitive graphs of valency 4, European J. Combin. 19 (1998) 345--354.
C.E. Praeger, Finite normal edge-transitive Cayley graphs, Bull. Aust. Math. Soc. 60 (1999) 207--220.
A.A. Talebi, Some normal edge-transitive Cayley graphs on dihedral groups, J. Math. Computer Sci. 2 (2011) 448--452.
C.Q. Wang, D.J. Wang and M.Y. Xu, On normal Cayley graphs of finite groups, Sci. China Math. 28 (1998) 131--139.
M.Y. Xu, Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math 182 (1998) 309--319.