Abstract
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.
Highlights
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
Resolving set and metric basis appeared on the scene way back in 1953 for an arbitrary metric space by Blumenthal [1]
Resolving sets play an important part in image proceeding and digital geometry
Summary
Resolving set and metric basis appeared on the scene way back in 1953 for an arbitrary metric space by Blumenthal [1]. 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. Let us denote by G, a simple connected graph, V be the set of vertices of graph, a metric d : V × V −→ W, where W is the set of non-negative integers and d(u, v) is the minimum number of edges in any path between u and v. Wk be an ordered set of vertices of G and let v be a vertex of G.
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