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has been cited by the following article:

• TITLE: Game Chromatic Number of Some Regular Graphs

  AUTHORS: Ramy Shaheen, Ziad Kanaya, Khaled Alshehada

  KEYWORDS: Game Chromatic Number, Circulant Graph, Generalized Petersen Graphs

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.9 No.4, October 28, 2019

  ABSTRACT: 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 byχg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic numberχg of circulant graphsCn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).