Metric basis and metric dimension of 1-pentagonal carbon nanocone networks

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 hav...

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Bibliographic Details
Published in:Scientific reports 2020-11, Vol.10 (1), p.19687-19687, Article 19687
Main Authors: Hussain, Zafar, Munir, Mobeen, Ahmad, Ashfaq, Chaudhary, Maqbool, Alam Khan, Junaid, Ahmed, Imtiaz
Format: Article
Language:English
Subjects:
Carbon
Chemistry
Combinatorial chemistry
Game theory
Mathematics
Robots
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-020-76516-1