A070995 Number of nonisomorphic (undirected) Cayley graphs for the group Zp x Zp, where Zp is the elementary Abelian group of order p and p is prime. The sequence is index by primes, though starts with 1.

1, 5, 50, 17794, 174685429024800, 1476099903835055889100, 569361345959217303084880851701375547158, 24894339520238610434672964029323166045198384692144, 221903632506534809770887023612289701531002339299063461384464526904412590996

Offset: 1

Author

Marni Mishna, May 18 2002

Keywords

• nonn

Comments

The formula comes from a cycle index; There is a similar formula for directed Cayley graphs

References

• C. Godsil, On Cayley graph isomorphisms, Ars, Combin., 15:231-246, 1983

Links

• B. Alspach and M. Mishna, Enumeration of Cayley graphs and digraphs, Discr. Math., 256 (2002), 527-539. [Note: In the third sum of Theorem 4.2 the exponent should be (p^2-1)/2/h(d). - _Sean A. Irvine_ and _Marni Mishna_, Jul 28 2024]
• Sean A. Irvine, Java program (github)
• M. Mishna, Cayley Graphs

Crossrefs

Cf. A049287.

Extensions

a(9) from Sean A. Irvine, Jul 22 2024