Graph coloring dates back to 1852, when Francis Guthrie come up with the four color conjecture. Gary Chartrand and Ping Zhang [3] discussed various colorings of graph and its properties in their book entitled Chromatic Graph Theory. A graph coloring is the assignment of a color to each of the vertices or edges or both in such a way that no two adjacent vertices and incident edges share the same color. Graph coloring has been applied to many real world problems like scheduling, allocation, telecommunications and bioinformatics, etc.

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