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Isomorphism testing for circulant graphs Cn(a,b)

Sara Nicoloso(nicoloso***at***disp.uniroma2.it)
Ugo Pietropaoli(pietropaoli***at***disp.uniroma2.it)

Abstract: 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.

Keywords: isomorphism, circulant graphs, Adam's conjecture

Category 1: Combinatorial Optimization (Graphs and Matroids )

Citation: Unpublished manuscript.

Download: [PDF]

Entry Submitted: 03/22/2010
Entry Accepted: 03/22/2010
Entry Last Modified: 03/22/2010

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