![]() ![]() The strong metric dimension of G, denoted by sdim ( G ), is defined as the cardinality of the strong metric basis. The strong metric basis of G is a strong resolving set with minimal cardinality. A set S ∈ V ( G ) is a strong resolving set if every two distinct vertices of G are strongly resolved by some vertex of S. ![]() A vertex s ∈ V ( G ) strongly resolves two vertices u and v if u belongs to a shortest v −s path, denoted by u ∈ I, or v belongs to a shortest u−s path, denoted by v ∈ I. The interval I between u and v is defined as the collection of all vertices that belong to some shortest u − v path. Let G be a connected graph with vertex set V ( G ) and edge set E ( G ).
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