Abstract:The metric representation of a vertex v of a graph G is a finite vector representing distances of v with respect to vertices of some ordered subset S⊆V (G). If no suitable subset of S provides separate representations for each vertex of V(G), then the set S is referred to as a minimal resolving set. The metric dimension of G is the cardinality of the smallest (with respect to its cardinality) minimal resolving set. A resolving set S is secure if for any v∈V–S, there exists x∈S such that (S–{x})∪{v} is a resolv… Show more
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