### The Characterization of Caterpillars with Multidimension 3

#### Abstract

Let v be a vertex of a connected graph G, and let W = {w1, w2, ..., wk} be a set of vertices of G. The multirepresentation of v with respect to W is the k-multiset mr(v|W) = {d(v,w1),d(v,w2),...,d(v,wk)}. A set W is called a multiresolving set of G if no two vertices of G have the same multirepresentations with respect to W. The multidimension of G is the minimum cardinality of a multiresolving set of G. In this paper, we characterize the caterpillars with multidimension 3.

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