The multiset partition dimension mpd(G) is at least 4 for every connected graph, equals 4 for paths, cycles with n≥9, grids, and ladders, and is infinite for complete, wheel, friendship, fan, and t-fold wheel graphs.
On the metric dimension of a graph,
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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.
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Multiset Partition Dimension of Graphs
The multiset partition dimension mpd(G) is at least 4 for every connected graph, equals 4 for paths, cycles with n≥9, grids, and ladders, and is infinite for complete, wheel, friendship, fan, and t-fold wheel graphs.
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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.