Identifying codes of cycles with odd orders

The problem of the rr-identifying code of a cycle CnCn has been solved totally when nn is even. Recently, S. Gravier et al. give the rr-identifying code for the cycle CnCn with the minimum cardinality for odd nn, when n≥3r+2n≥3r+2 and gcd(2r+1,n)≠1gcd(2r+1,n)≠1. In this paper, we deal with the rr-identifying code of the cycle CnCn for odd nn, when n≥3r+2n≥3r+2 and gcd(2r+1,n)=1gcd(2r+1,n)=1.