Sharp bounds for partition dimension of generalized Möbius ladders

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

Keywords

• metric dimension
• partition dimension
• generalized möbius ladder
• 05c12
• 05c15
• 05c78