please do all parts

The goal of this problem is to investigate relationships between the chromatic number of the join of two graphs and the chromatic numbers of the individual graphs. (a) Draw C3+C4 and find a minimal proper vertex coloring. Explain why the coloring you found uses as few colors as possible. (b) In a proper vertex coloring of Cp+Cq, can a vertex of Cp and a vertex of Cq share the same color? Why or why not? (c) Find the chromatic number of the graph Cp+Cq. (Hint: Consider cases depending on the parities of p and q. The goal of this problem is to investigate relationships between the chromatic number of the join of two graphs and the chromatic numbers of the individual graphs. (a) Draw C3+C4 and find a minimal proper vertex coloring. Explain why the coloring you found uses as few colors as possible. (b) In a proper vertex coloring of Cp+Cq, can a vertex of Cp and a vertex of Cq share the same color? Why or why not? (c) Find the chromatic number of the graph Cp+Cq. (Hint: Consider cases depending on the parities of p and