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

Abstract

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 χg(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 Pn and cycle Cn for n≥5 is 4. We also answer a question posed by Xuding Zhu in [12] for the splitting graphs of path Pn and n-cycle for all n≥3