The Multibases of Symmetric Caterpillars

Abstract

For a set W=w1,w2,.,wk of vertices and a vertex v of a connected graph G, the k-multiset mrvW=dv,w1,dv,w2,.,dv,wk, where dv,wi is the distance from v to wi for i=1,2,.,k, and is the multirepresentation of v with respect to W. The set W is a multiresolving set of G if the multirepresentations of every two distinct vertices of G with respect to W are distinct. The multiresolving set of G having the minimum cardinality is called a multibasis of G. The cardinality of a multibasis of G is the multidimensiondimMG of G. A caterpillar cak1,k2,.,ks is called a symmetric caterpillar if ki=ks-i+1 for all integers i with 1≤i≤s. In this work, the multiresolving sets of symmetric caterpillars are studied. © 2020 Supachoke Isariyapalakul et al.