Abstract:Abstract:Metric dimension or location number is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs G n : F = (G n ) n≥1 depending on n as follows: the order |V (G)| = ϕ(n) and lim n→∞ ϕ(n) = ∞. If there exists a constant C > 0 such that dim(G n ) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwise F has unbounded metric dimension. If all graphs in F have the same metric dimension (which does n… Show more
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