On the enumeration of circulant graphs of prime-power order : the case of p3

Abstract

A well-known problem in Algebraic Combinatoric, in the enumeration of circulant graphs. The failure of Adam's Conjecture for such graphs with order containing a repeated prime, led researchers to investigate the problem using two different methods, namely the multiplier method and the structural method. The former makes use of isomorphism theorems whereas the latter involves Schur rings. Both these methods have already been used to count the number of non isomorphic circulants of order p2 . This research focuses on the extension of these two methods to enumerate circulants of order p3 , in particular for p = 3 and p = 5, through the use of the computer package GAP.