https://doi.org/10.1140/epje/s10189-025-00471-w
Regular Article - Living Systems
Vertex-based parameters of hierarchal lattice tube with an application of metric dimension
1
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11623, Riyadh, Saudi Arabia
2
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, 45142, Jazan, Kingdom of Saudi Arabia
3
Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
4
Department of Mathematics, Riphah International University, 54000, Lahore, Pakistan
Received:
3
May
2024
Accepted:
24
December
2024
Published online:
28
January
2025
Architectural metamaterials that span different length scales and are either self-similar or dissimilar to one another make up hierarchical lattices. Comparing hierarchical lattices to traditional ones reveals that they offer superior and customizable properties, which allows for a wide variety of material property manipulation and optimization. Each computer network can be represented as a graph, where nodes alternate as vertices and links are edges. The recent advanced topic of resolvability parameters of a graph involves shaping the entire structure to obtain each nodes’ specific position. In this article, we computed the metric, fault metric, and partition dimension of the hierarchal lattic tube. The application of the metric dimension is also covered in this paper.
Mathematics Subject Classification: 74F25 / 74E40 / 05C90 / 05C70 / 05C50 / 05C10.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.