Bounds on the Partition Dimension of Convex Polytopes

(E-pub Ahead of Print)

Author(s): Jia-Bao Liu, Muhammad Faisal Nadeem*, Mohammad Azeem

Journal Name: Combinatorial Chemistry & High Throughput Screening
Accelerated Technologies for Biotechnology, Bioassays, Medicinal Chemistry and Natural Products Research


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Abstract:

Aims and Objective: The idea of partition and resolving sets plays an important role in various areas of engineering, chemistry and computer science such as robot navigation, facility location, pharmaceutical chemistry, combinatorial optimization, networking, and mastermind game.

Method: In a graph to obtain the exact location of a required vertex which is unique from all the vertices, several vertices are selected this is called resolving set and its generalization is called resolving partition, where selected vertices are in the form of subsets. Minimum number of partitions of the vertices into sets is called partition dimension.

Results: It was proved that determining the partition dimension a graph is nondeterministic polynomial time (NP) problem. In this article, we find the partition dimension of convex polytopes and provide their bounds.

Conclusion: The major contribution of this article is that, due to the complexity of computing the exact partition dimension we provides the bounds and show that all the graphs discussed in results have partition dimension either less or equals to 4, but it cannot been be greater than 4.

Keywords: Partition dimension, resolving partition, resolving sets, convex polytopes, bounded partition dimension

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Article Details

Published on: 04 December, 2020
(E-pub Ahead of Print)
DOI: 10.2174/1386207323666201204144422
Price: $95

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