1. (10 pts) Design a polynomial-time algorithm for the graph 2-coloring problem, which whether vertices of a given graph can be colored in no more than two colors so that no two adjacent vertices are colored the same color. (a) Generate two sample graphs to demonstrate how your algorithm performs. You should have one graph where a 2-coloring exists and one graph where it doesn't exist. Explain how your algorithm performs on each graph. Include your graphs in your assignment submission