Bounds for partition dimension of M-wheels

Abstract

Resolving partition and partition dimension have multipurpose applications in computer, networking, optimization, mastermind games and modelling of chemical substances. The problem of finding exact values of partition dimension is hard so one can find bound for the partition dimension of a general family of graph. In the present article, we give the sharp upper bounds and lower bounds for the partition dimension of m-wheel, Wn,m for all n ≥ 4 and m ≥ 1. Presented data generalise some already available results.