On the partition dimension and connected partition dimension of wheels

Abstract

Let G be a connected graph. For a vertex v ∈ V (G) and an ordered k-partition Π = {S1, S2, ..., Sk} of V (G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v, S1), d(v, S2), ..., d(v, Sk)). The k-partition Π is said to be resolving if the k-vectors r(v|Π), v ∈ V (G), are distinct. The minimum k for which there is a resolving k… (More)

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