The outer multiset dimension \({\rm dim}_{\rm ms}(G)\) of a graph \(G\) is the cardinality of a smallest set of vertices that uniquely recognize all the vertices outside this set by using multisets of distances to the set. It is proved that \({\rm dim}_{\rm ms}(G) = n(G) - 1\) if and only if \(G\) is a regular graph with diameter at most \(2\). Gra...

Further contributions on the outer multiset dimension of graphs