Sharp bounds for partition dimension of generalized Möbius ladders

The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing. It is hard to compute exact values of partition dimension for a graphic metric space, ( , ) and networks. In this...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2018-11, Vol.16 (1), p.1283-1290
Main Authors: Hussain, Zafar, Khan, Junaid Alam, Munir, Mobeen, Saleem, Muhammad Shoaib, Iqbal, Zaffar
Format: Article
Language:English
Subjects:
05C12
05C15
05C78
Generalized Möbius Ladder
Ladders
Lower bounds
Metric dimension
Metric space
Optimization
Partition dimension
Upper bounds
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Summary:The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing. It is hard to compute exact values of partition dimension for a graphic metric space, ( , ) and networks. In this article, we give the sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, , for all ≥3 and ≥2.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2018-0109