Geodesic
Block Graphs with Large Paired Domination Multisubdivision Number
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 665-684

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The paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
Keywords: paired domination, domination subdivision number, domination multisubdivision number, block graph 
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     author = {Mynhardt, Christina M. and Raczek, Joanna},
     title = {Block {Graphs} with {Large} {Paired} {Domination} {Multisubdivision} {Number}},
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Mynhardt, Christina M.; Raczek, Joanna. Block Graphs with Large Paired Domination Multisubdivision Number. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 665-684. http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a19/