On the Enumeration of Circulant Graphs of Prime-Power Order: the case of p³

2017/03/17 by Victoria Gatt, Gatt, Victoria
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1703.06038

openalex publication_date 2017/03/17 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

A well-known problem in Algebraic Combinatorics, is 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.

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