Locating and Identifying Codes in Circulant Graphs

Abstract

Identifying and locating-dominating codes have been studied widely in circulant graphs. Recently, Ville Junnila et al. (Optimal bounds on codes for location in circulant graphs, Cryptography and Communications; 2019) studied identifying and locating-dominating codes in circulants $C_n\left(1,d\right)$ , $C_n\left(1,d-1,d\right)$ , and $C_n\left(1,d-1,d,d+1\right)$ . In this paper, identifying, locating, and self-identifying codes in the circulant graphs $C_n\left(k,d\right)$ , $C_n\left(k,d-k,d\right)$ , and $C_n\left(k,d-k,d,d+k\right)$ are studied, and this extends Junnila et al.’s results to general cases.