Consider the Vertex Coloring Problem in which we assign different colors to the adjacent vertices on a given graph G = (V, E). The objective is to color the vertices of the graph using minimum number of colors. Input: A graph G = (V, E), where V is the set of vertices and E is the set of edges of the graph G. Output: Color assignments of the vertices using minimum number of colors. 1. 2. 3. 4. v6 v4 Figure 1: Vertex color assignment on a graph G Discuss the problem complexity of the Vertex Coloring Problem. Is it in Por NP? Is it an easy or a hard problem? Design a greedy algorithm that solves the Vertex Coloring Problem using a greedy color selection rule. Report the pseudocode of your algorithm. What is the time complexity of your algorithm? Is it efficient? Can your algorithm find the optimum solution? Implement your algorithm in Python. Use the input given in the example and report the console outputs. Report your Python code scripts.