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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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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creator Hussain, Zafar
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description 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.
doi_str_mv 10.1515/math-2018-0109
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source Publicly Available Content Database; De Gruyter Open Access Journals
subjects 05C12
05C15
05C78
Generalized Möbius Ladder
Ladders
Lower bounds
Metric dimension
Metric space
Optimization
Partition dimension
Upper bounds
title Sharp bounds for partition dimension of generalized Möbius ladders
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