The Multibases of Symmetric Caterpillars

الملخص EN

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.