Game chromatic number class graphs (Cm ⊙ Kn) and (Sm ⊙ Kn) of corona operation result
Fitria Puspa Dewi, Riduan Yusuf, Abdul Mujib, Firmansyah Firmansyah · AIP conference proceedings · 2024
Given graph G and color set c. Supposed A is the first player who tries to color all the vertex of the graph. Lets's say B is the second player who tries to at least one vertex in G can't be colored. The game chromatic number of graph G is defined as the smallest k number such that A has a winning strategy on the graph G with k colors, denoted χg (G). The graph itself is a set of the vertex that is connected, for the application of the graph itself, we can create transportation paths using the graph method, model an online game using graph theory, graph theory in traffic lights, and so on. This study examines the corona operation graph class (Cm ⊙ Kn) and (Sm ⊙ Kn). The method used in this research is exploratory qualitative research, which aims to develop and find a new theory about game chromatic numbers. The result of the research is that the generalization of the chromatic number of the graph class game χg(Cm⊙Kn)={ 3if n=1n+2if n≥2 and the graph class χg (Sm ⊙ Kn) = n + 2.