Isomorphism testing for circulant graphs
نویسندگان
چکیده
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.
منابع مشابه
Testing set proportionality and the Ádám isomorphism of circulant graphs
Given two k element subsets S,T ⊆ Zn, we give a quasi-linear algorithm to either find λ ∈ Z∗n such that S = λT or prove that no such λ exists. This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature. © 2005 Elsevier B.V. All rights reserved.
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