Exploring metric dimensions in chemical structures: Insights and applications

Chaudhry F., Farooq U., Maktoof M. A. J., Mousa S. H., Farahani M. R., Alaeiyan M., ...More

Journal of Discrete Mathematical Sciences and Cryptography, vol.28, no.2, pp.491-509, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.47974/jdmsc-2248
  • Journal Name: Journal of Discrete Mathematical Sciences and Cryptography
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.491-509
  • Keywords: Backbone DNA network, Bakelite network, Graph theory, Lattice networks, Metric dimension, Organic electronics, Polythiophene network, Vertex identification
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this article, we dive into the metric dimension of various lattice networks, focusing on Bakelite, Backbone DNA, and Polythiophene networks. The metric dimension is a crucial graph invariant that helps us understand how uniquely we can identify the vertices in a network. Our detailed analysis and calculations reveal that the metric dimension for Bakelite, Polythiophene, and Backbone DNA networks is consistently two. This means that, within these lattice structures, a simple pair of vertices is enough to pinpoint the location of all other vertices. These insights shed light on the structural properties of these molecular networks and could have practical implications for areas like biological systems and organic electronics. Plus, this study sets the stage for future research in graph theory and the understanding of molecular structures.