Isomorphism testing for circulant graphs Cn(a,b)

In this paper we focus on connected directed/undirected circulant graphs Cn(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 Cn(a, b) and Cn(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, b)} = {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.