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

TL;DR

This paper introduces a new structural model for crystal cubic carbon and determines the minimum sizes of doubly resolving and strong resolving sets for it.

Contribution

It provides the first determination of minimum resolving set sizes for the crystal cubic carbon using an innovative structural representation.

Findings

Minimum doubly resolving set size for CCC(n) determined.

Minimum strong resolving set size for CCC(n) determined.

New structural model for crystal cubic carbon introduced.

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 $CCC(n)$.