A Minimum Doubly Resolving Set and Strong Resolving Set for the Crystal Cubic Carbon

Abstract

The task of identifying resolving sets has been extensively studied due to its wide relevance in fields such as chemistry, robot navigation, combinatorial optimization, pattern recognition, and image processing. These applications have helped motivate and establish the theoretical foundations of the subject. Notably, problems of this type are generally known to be NP-hard. This study introduces an alternative structural representation for the crystal cubic carbon \( CCC(n) \). Building on this model, we determine the minimum sizes of both a doubly resolving set and a strong resolving set for $CCC(n)$.