Let
G be a graph and
k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of
G with a set of
k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the
k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by
χg(G), is the smallest
k such that Alice has a winning strategy with
k colors. In this paper, we determine the game chromatic number
χg of circulant graphs
Cn(1,2),
, and generalized Petersen graphs
GP(
n,2),
GP(
n,3).