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Computation of Edge Resolvability of Benzenoid Tripod Structure

Author

Listed:
  • Ali Ahmad
  • Sadia Husain
  • Muhammad Azeem
  • Kashif Elahi
  • M. K. Siddiqui
  • Gaetano Luciano

Abstract

In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively. Edge resolving set λe is an ordered subset of nodes of a graph C, in which each edge of C is distinctively determined by its distance vector to the nodes in λ. The cardinality of a minimum edge resolving set is called the edge metric dimension of C. An edge resolving set Le,f of C is fault-tolerant if λe,f∖b is also an edge resolving set, for every b in λe,f. Resolving set allows obtaining a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. In this paper, we determine the exact edge metric and fault-tolerant edge metric dimension of benzenoid tripod structure and proved that both parameters are constant.

Suggested Citation

  • Ali Ahmad & Sadia Husain & Muhammad Azeem & Kashif Elahi & M. K. Siddiqui & Gaetano Luciano, 2021. "Computation of Edge Resolvability of Benzenoid Tripod Structure," Journal of Mathematics, Hindawi, vol. 2021, pages 1-8, October.
    • Handle: RePEc:hin:jjmath:9336540
    DOI: 10.1155/2021/9336540
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