On Strong Metric Dimension of Cubic Carbon Crystal

• Published in: International journal of applied and computational mathematics Vol. 11; no. 3
• Main Authors: Singh, Malkesh, Sharma, Sunny Kumar, Bhat, Vijay Kumar
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2025; Springer Nature B.V
• Subjects: Apexes; Applications of Mathematics; Carbon; Carbon compounds; Chemical bonds; Chemical compounds; Chemical properties; Chemistry; Computational Science and Engineering; Eigenvalues; Environmental chemistry; Graph theory; Lower bounds; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Molecular structure; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Parameter identification; Theoretical; 05C10; 05C12; Molecular graph; Chemical compound; Crystal cubic carbon; Strong resolving set; Strong metric dimension; 68R10; Resolvability parameters
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01893-y

Computation of any numerical characteristic of a molecular graph results in understanding the properties of the respective chemical compound. A molecular graph is the graph of a chemical compound, in which atoms are presented in the form of vertices and the bonds between the atoms are the edges of the graph. These chemical graphs play a vital role in balancing the connection between two domains, viz., graph theory and chemistry. Investigating the graph of a molecule aids in the development of applications and theoretical research for the chemical compound in mathematical chemistry. The rigorous analysis of a complex molecular graph provides insight in understanding the molecular structure, biological interactions, environmental chemistry, nanotechnology, molecular isomerism, various physio-chemical properties, material related science, and wide-ranging applications in drug design. Studying these properties of a chemical compound by considering its structural representation and examining it from every aspect (graph variants like, distance-based, degree-based, eigenvalue-based, etc.) has various applications and is of great significance nowadays. One such graph-theoretic distance-related variant pertains to the parameters of the resolvability (metric dimension, strong metric dimension, edge metric dimension, partition dimension, etc.). These parameters help in identifying all the elements (vertices and/or edges) of graph in a unique way, based on certain characteristics related to distances between the elements. In this paper, we consider an important class of a carbon-based compound, known as Crystal Cubic Carbon (CCC), and explore some of the resolvability parameters for it. In particular, we investigate upper and lower bounds on its strong resolving set, strong metric basis, and the corresponding strong metric dimension of CCC. Furthermore, we perform various comprehensive analyses including comparison with other parameters of resolvability to deepen the knowledge of its structural and physio-chemical properties.