Game Chromatic Number of Shackle Graphs

Abstract

Coloring vertices on graph is one of the topics of discrete mathematics that are still developing until now. Exploration Coloring vertices develops in the form of a game known as a coloring game. Let G graph. The smallest number k such that the graph G can be colored in a coloring game is called game chromatic number. Notated as χg(G). The main objective of this research is to prove game chromatic numbers from graphs shack(Kn, vi ,t),shack(Sn, vi , t), and shack(Kn,n, vi ,t). The research method used in this research is qualitative. The result show that χg(shack(Kn, vi ,t)) = n, and χg(shack(Sn, vi , t)) = χg (shack(Kn,n, vi ,t)) = 3. The game chromatic number of the shackle graph depends on the subgraph and linkage vertices. Therefore, it is necessary to make sure the vertex linkage is colored first.