Chromatic index of graph 3 coloring is given by Y’ (S) of the graph ‘S’.
So we can represent the graph 3 coloring as function F: X ® Y.
Where the coloring of the vertexes of graph ‘S’ is map and adjacent vertices has the distinct color in ‘Y’, and a b Î E, then F (a) ≠ F (b).
The graph 3 coloring can be expressed as S = (X, Y), where ‘S’ represents the graph.
‘X’ represents the vertices and ‘Y’ represents the edges of the graph.
Applications of graph 3 coloring are:
1. It is used in the puzzle of Sudoku for the specification of the graph.
2. It is also used in pattern matching of the graph.
Example of graph 3 coloring is given below:
Suppose that, we have drawn a triangle inside a pentagon in such a way that we have three Triangles inside a pentagon. We have to color the vertex of the graph with three colors in such a way that no two adjacent vertexes have same color.