On the game chromatic number of splitting graphs of path and cycle.

Given a graph G and an integer k , two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins if at the end of the game all the vertices of G are colored. The game chromatic number χ g (G) is the minimum k for which the first player has a winning strategy. In this study, we prove that the game chromatic number of the splitting graphs of the path P n and cycle C n for n ≥ 5 is 4. We also answer a question posed by Xuding Zhu in [12] for the splitting graphs of path P n and n -cycle for all n ≥ 3 [ABSTRACT FROM AUTHOR]