An Elementary Abelian Group of Rank 4 Is a CI-Group

In this paper we prove that Z4p is a CI-group; i.e., two Cayley graphs over the elementary abelian group Z4p are isomorphic if and only if their connecting sets are conjugate by an automorphism of the group Z4p.

[1]  Cai Heng Li,et al.  Finite CI‐Groups are Soluble , 1999 .

[2]  Cheryl E. Praeger,et al.  On the Isomorphism Problem for Finite Cayley Graphs of Bounded Valency , 1999, Eur. J. Comb..

[3]  E. Bannai,et al.  Algebraic Combinatorics I: Association Schemes , 1984 .

[4]  Cai Heng Li.  On Isomorphisms of Connected Cayley Graphs, II , 1998, J. Comb. Theory, Ser. B.

[5]  Mikhail E. Muzychuk,et al.  Ádám's Conjecture is True in the Square-Free Case , 1995, J. Comb. Theory, Ser. A.

[6]  László Babai,et al.  Isomorphism problem for a class of point-symmetric structures , 1977 .

[7]  Cai Heng Li,et al.  On Isomorphisms of Finite Cayley Graphs , 1998, Eur. J. Comb..

[8]  Mikhail E. Muzychuk,et al.  On Ádám's conjecture for circulant graphs , 1997, Discret. Math..

[9]  Olaf Tamaschke.  A generalization of conjugacy in groups , 1968 .

[10]  H. Wielandt,et al.  Permutation groups through invariant relations and invariant functions , 1969 .

[11]  Brian Alspach,et al.  Isomorphism of circulant graphs and digraphs , 1979, Discret. Math..

[12]  Cai Heng Li.  On isomorphisms of connected Cayley graphs , 1998, Discret. Math..

[13]  Cai Heng Li.  The finite groups with the 2-dci property , 1996 .

[14]  G. Sabidussi.  Vertex-transitive graphs , 1964 .

[15]  Cai Mao-cheng,et al.  A degree condition for a graph to have [ a, b ]-factors , 1998 .

[16]  Paul-Hermann Zieschang,et al.  An Algebraic Approach to Association Schemes , 1996 .

[17]  Chris D. Godsil,et al.  ALGEBRAIC COMBINATORICS , 2013 .

[18]  Edward Dobson,et al.  Isomorphism problem for Cayley graphs of Zp3 , 1995, Discret. Math..

[19]  Eiichi Bannai,et al.  Character Tables of Fission Schemes and Fusion Schemes , 1993, Eur. J. Comb..

[20]  Cheryl E. Praeger,et al.  On finite groups with the cayley isomorphism property , 1998, J. Graph Theory.

[21]  B. Elspas,et al.  Graphs with circulant adjacency matrices , 1970 .

[22]  D. Ź. Djoković.  Isomorphism problem for a special class of graphs , 1970 .

[23]  Cheryl E. Praeger,et al.  On finite groups with the Cayley isomorphism property , 1998 .

[24]  Peter Frankl,et al.  Isomorphisms of Cayley graphs. II , 1979 .