Isomorphism testing for circulant graphs C n(a, b)

Abstract

In this paper we focus on connected directed/undirected circulant graphs C _n(a,b). We investigate some topological characteristics, and define a simple combinatorial model, which is new for the topic. Building on such a model, we derive a necessary and sufficient condition to test whether two circulant graphs C _n(α,b) and C _n(a',b') are isomorphic or not. The method is entirely elementary and consists of comparing two suitably computed integers in {1,.....n/gcd(n,a) gcd(n,b) - 1}, and of verifying if {gcd(n,a),gcd(n,6)} = {gcd(n, a'),gcd(n, b')}, It also allows for building the mapping function in linear time. In addition, properties of the classes of mutually isomorphic graphs are analyzed.