Make the python code for the below problem to plot the final graph of time vs size to get the best case, average case and worst case graph of backtracking algorithm in graph coloring problem. You have to make the dataset of input graphs that will increase in size gradually and plot the graph to get the time complexity graph Backtracking Algorithm Comparison in Graph Coloring Problem

Graph Coloring Problem:

Graph Coloring is a technique of coloring vertices on a graph so that no neighboring nodes have the same color. The problem is$,$ given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color.

Analyze Backtracking Algorithm to solve Graph coloring problem with different number of Vertices