Proves multiset resolving sets equal ID-colorings, establishes NP-completeness of computing multiset dimension, bounds it by 4 on king grids, and characterizes when it is finite on certain strong products.
Metric dimension related parameters in graphs: A survey on combinatorial, computa- tional and applied results, arXiv:2107.04877 [math.CO] (10 Jul 2021)
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The weak k-metric dimension of the direct product of two isomorphic complete graphs is computed exactly for almost all cases with a bound given for the rest.
Geodetic graphs minimize the geodesic subpath number while an upper bound is established for general graphs on n vertices and extremal structures are characterized among cactus graphs.
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Complexity and equivalency of multiset dimension and ID-colorings
Proves multiset resolving sets equal ID-colorings, establishes NP-completeness of computing multiset dimension, bounds it by 4 on king grids, and characterizes when it is finite on certain strong products.