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Updated: Nov 30, 2025

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Published on: December 6, 2021
Metric basis and metric dimension of 1-pentagonal carbon nanocone networks
Zafar Hussain1, Mobeen Munir2, Ashfaq Ahmad3
1Department of Mathematics and Statistics, The University of Lahore, Lahore, 54000, Pakistan.
Abstract:
Resolving set and metric basis has become an integral part in combinatorial chemistry and molecular topology. It has a lot of applications in computer, chemistry, pharmacy and mathematical disciplines. A subset S of the vertex set V of a connected graph G resolves G if all vertices of G have different representations with respect to S. A metric basis for G is a resolving set having minimum cardinal number and this cardinal number is called the metric dimension of G. In present work, we find a metric basis and also metric dimension of 1-pentagonal carbon nanocones. We conclude that only three vertices are minimal requirement for the unique identification of all vertices in this network.
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