Geodesic
Domination game: Effect of edge contraction and edge subdivision
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 313-329

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In this paper the behavior of the game domination number γ_g(G) and the Staller start game domination number γ_g^'(G) by the contraction of an edge and the subdivision of an edge are investigated. Here we prove that contracting an edge can decrease γ_g(G) and γ_g^'(G) by at most two, whereas subdividing an edge can increase these parameters by at most two. In the case of no-minus graphs it is proved that subdividing an edge can increase both these parameters by at most one but on the other hand contracting an edge can decrease these by two. All possible values of these parameters are also analysed here.
Keywords: domination game, edge contraction, edge subdivision 
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     title = {Domination game: {Effect} of edge contraction and edge subdivision},
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James, Tijo; Vijayakumar, Ambat. Domination game: Effect of edge contraction and edge subdivision. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 313-329. http://geodesic.mathdoc.fr/item/DMGT_2023_43_2_a1/