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)
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the highest interest for the research community dealing with several variants of metric dimension in graphs.
representative citing papers
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.
The paper defines the geodesic subpath number and claims an upper bound for it, but the bound is violated by simple graphs such as P3 and K5−e.
A literature survey consolidates results on multiset dimension and its local/outer/edge variants and proposes new multiset partition and related parameters as open directions.
citing papers explorer
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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.
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The weak $k$-metric dimension of the direct product of complete graphs
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.
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Counting geodesic paths in graphs
The paper defines the geodesic subpath number and claims an upper bound for it, but the bound is violated by simple graphs such as P3 and K5−e.
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A Survey on Multiset Dimension and Its Variations
A literature survey consolidates results on multiset dimension and its local/outer/edge variants and proposes new multiset partition and related parameters as open directions.