Edge multiset dimension of subdivided complete graphs
An edge of a graph can be identified by its distances to a suitable set of vertices. If the reports omit the names of these vertices, only a multiset of distances remains, and finding a suitable set becomes more difficult. We determine the asymptotic cost of this loss of information for subdivided complete graphs. Let \(K_n\) be the complete graph on \(n\ge3\) vertices, and let \(S_L(K_n)\) replace each edge with a path of \(L\) edges, where \(L\ge2\) is an integer. Let \(\operatorname{edim}_{\mathrm m}\) be the minimum number of vertices whose distance multisets distinguish all edges. For…
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