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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

On metric dimension of circumcoronene series of benzenoid networks

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* Corresponding author · click or hover a name for details

pp. 511–524Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-2249 Crossmark XML
Received:
04 Feb 2025
Published Online:
11 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2249
Pages:
511–524

Abstract

In molecular topology and chemistry, resolving sets and metric bases are essential concepts. They have numerous applications in computer science, artificial intelligence, chemistry, pharmacy, traffic networking, mathematical modeling, and programming. Adivision S of the vertex set χ of a linked graph G is said to resolve G if eachpoint of G can be represented from its neighborhood in S. A metric dimension of a graph is the number of the smallest resolving set, also known as the metric basis of the graph.In the current research we will determine the metric dimension and metric basis of the circumcoronene series CS of benzenoid Hk for k ≥ 1. We prove that a set with three vertices is required to resolve this graph, and therefore, its metric dimension is 3.

Keywords

Subject Classifications

05C1205C7605C9068R10

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