Sharp bounds for partition dimension of generalized Möbius ladders

Abstract

Abstract 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, ( G , d G ) and networks. In this article, we give the sharp upper bounds and lower bounds for the partition dimension of generalized Möbius ladders, M m , n , for all n ≥3 and m ≥2.