The isomorphism problem for rose window graphs

Given integers n≥3 and 1≤a,r≤n−1 with r≠n/2, the rose window graph Rn(a,r) is the graph with vertex set {Ai,Bi|i∈{0,1,…,n−1}} and edges {Ai,Ai+1},{Ai,Bi},{Ai+a,Bi} and {Bi,Bi+r} for every i∈{0,1,…,n−1} where addition in subscripts is modulo n. In this paper we give necessary and sufficient conditions for two rose window graphs to be isomorphic.