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The characterization of caterpillars with multidimension 3. (English) Zbl 1463.05138

Summary: Let \(v\) be a vertex of a connected graph \(G\), and let \(W = \{w_1, w_2,\dots, w_k\}\) be a set of vertices of \(G\). The multirepresentation of \(v\) with respect to \(W\) is the \(k\)-multiset \(mr(v|W) = \{d(v,w_1),d(v,w_2),\dots,d(v,w_k)\}\). 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.

MSC:

05C12 Distance in graphs
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