On graphs with largest possible game domination number

Let γ(G) and γg(G) be the domination number and the game domination number of a graph G, respectively. In this paper γg-maximal graphs are introduced as the graphs G for which γg(G)=2γ(G)−1 holds. Large families of γg-maximal graphs are constructed among the graphs in which their sets of support vertices are minimum dominating sets. γg-maximal graphs are also characterized among the starlike trees, that is, trees which have exactly one vertex of degree at least 3.