The Characterization of Caterpillars with Multidimension 3
Varanoot Khemmani, Supachoke Isariyapalakul · Thai Journal of Mathematics · 2020
Let v be a vertex of a connected graph G , and let W = { w 1 , w 2 , ..., 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 ) ,...,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.