A Preliminary Concept on Graph Coloring

This paper introduces the new study about combining the concept of Coloring with Fractal Graphs. Fractal Graph is the famous graph which has self-similarity property included it. It is developed in many areas and has much application in various engineering fields like computer science, Physical, Medical etc. Coloring is the advanced tool of Graph Theory. Its application is growing in various fields. Coloring the vertices is nothing but give the color to each vertices. Adjacent vertices are not colored by the same. Terminal vertices of each edge are colored by different colors like green, blue, yellow, red etc. Chromatic Number is the number of colors needed to the graph for coloring the vertices. It is denoted by CN (G). This paper analyses the chromatic number of various graphs Null Graph, Trivial Graph, Complete Graph, Star Graph, and Wheel Graph and also self-similarity fractal graph like Cantor Set Von Koch Curve. This paper found that the constant ratio of number of colors needed for coloring the above graphs.