Geodesic
Graphs with Unique Maximum Packing of Closed Neighborhoods
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 779-797

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A packing of a graph G is a subset P of the vertex set of G such that the closed neighborhoods of any two distinct vertices of P do not intersect. We study graphs with a unique packing of the maximum cardinality. We present several general properties for such graphs. These properties are used to characterize the trees with a unique maximum packing. Two characterizations are presented where one of them is inductive based on five operations.
Keywords: unique maximum packing, closed neighborhoods, trees 
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     author = {Bo\v{z}ovi\'c, Dragana and Peterin, Iztok},
     title = {Graphs with {Unique} {Maximum} {Packing} of {Closed} {Neighborhoods}},
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Božović, Dragana; Peterin, Iztok. Graphs with Unique Maximum Packing of Closed Neighborhoods. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 779-797. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a6/