FEATURE/Addition_of_Graph_Coloring_Problem_in_Graphs_directory

[harshika0926]

Description of Change

Issue [FEATURE] Addition of Graph Coloring Problem in Graphs directory #2617 Proposal Addition of Graph Coloring Problem algorithm under in Graphs directory

Overview The graph coloring problem asks to assign colors to the vertices of a graph in such a way that no two adjacent vertices share the same color. The objective is often to color the graph with as few colors as possible.

Issue details The greedy coloring algorithm is a straightforward approach to solve this problem. Here's a basic outline of the greedy algorithm:

Ordering the Vertices: Although not strictly necessary, the algorithm can start by ordering the vertices in some fashion. Different orderings may produce different results. A common ordering is by the degree of the vertices, but the simplest is just the order in which the vertices are given. Coloring: Start with the first vertex and assign it the first color. Then move to the next vertex. For each subsequent vertex, look at its neighbors and determine what colors have already been assigned. Assign the smallest possible color that hasn't been used by its neighbors.

More Details https://en.wikipedia.org/wiki/Graph_coloring

Context This change is crucial as it addresses a common problem in graph theory solved using greedy approach, enhancing the repository's comprehensiveness

Checklist

• [ x] Added description of change
• [ x] Added file name matches File name guidelines
• [x ] Added tests and example, test must pass
• [ x] Added documentation so that the program is self-explanatory and educational - Doxygen guidelines
• [x ] Relevant documentation/comments is changed or added
• [ x] PR title follows semantic commit guidelines
• [ x] Search previous suggestions before making a new one, as yours may be a duplicate.
• [ x] I acknowledge that all my contributions will be made under the project's license.

Notes:

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