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 multirepresenta-tions 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. © 2020 by the Mathematical Association of Thailand.