Domination game: Effect of edge contraction and edge subdivision

Abstract

In this paper the behavior of the game domination number γg(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 γg(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.