The domination game played on diameter 2 graphs

Abstract

Let γ g (G) be the game domination number of a graph G. It is proved that11 . The bound is attained: if diam(G) = 2 and n(G) ≤ 10, then γ g (G) = n(G) 2 if and only if G is one of seven sporadic graphs with n(G) ≤ 6 or the Petersen graph, and there are exactly ten graphs of diameter 2 and order 11 that attain the bound.