Game Chromatic Number of Some Regular Graphs  

作　　者：Ramy Shaheen Ziad Kanaya Khaled Alshehada 

机构地区：[1]Department of Mathematics, Tishreen University, Lattakia, Syria

出　　处：《Open Journal of Discrete Mathematics》2019年第4期159-164,共6页离散数学期刊（英文）

摘　　要：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).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).

关 键 词：GAME CHROMATIC NUMBER CIRCULANT GRAPH Generalized Petersen GRAPHS 

分 类 号：O15[理学—数学]