Java is the required programming language

To address the impending STEM shortage early on, your local elementary school decided to teach graph theory to its kindergarten students! To tap into their age-specific skills, the students are asked to color the vertices ofa graph with colors of their own choosing. There is one constraint, however: they cannot use the same color for two vertices if those vertices are connected by an edge Furthermore, they are asked to use as few different colors as possible. The illustration shows a few examples of student work. t- A 3 2 2 3 There is one problem, as you can imagine: there is no money to train teachers to grade these students' submissions! Thus, your task is to write a program that computes the sample solutions for the graphs given on each work sheet! Input The input consists of a description of a single graph. The first line contains a number N (2