The multibases of symmetric caterpillars (Q2194675)

Summary: For a set \(W=\{ w_1 , w_2 , \dots , w_k\}\) of vertices and a vertex \(v\) of a connected graph \(G\), the \(k\)-multiset \(mr(v|W)=\{d(v,w_1), d (v,w_2),\dots, d (v,w_k)\}\), where \(d(v,w_i)\) is the distance from \(v\) to \(w_i\) for \(i=1,2,\dots,k\), and is the \textit{multirepresentation} of \(v\) with respect to \(W\). The set \(W\) is a \textit{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 \textit{multibasis} of \(G\). The cardinality of a multibasis of \(G\) is the multidimension \(\dim_M(G)\) of \(G\). A caterpillar \(\mathrm{ca}(k_1, k_2,\dots, k_s)\) is called a \textit{symmetric caterpillar} if \(k_i= k_{s-i+1}\) for all integers \(i\) with \(1\leq i\leq s\). In this work, the multiresolving sets of symmetric caterpillars are studied.