Sales Toll Free No: 1-800-481-2338

# Graph 3 Coloring

TopIn 3- graph coloring, we color each node of the graph using three colors. The colors used in graph 3 coloring are red, green and blue. Graph 3 coloring is defined as the coloring of the vertex of the graph in such a manner that no two adjacent vertexes have same color. It can also be defined, as the way of coloring the vertexes of the graph. Three colors are used in graph 3 coloring in order to avoid graph 3 coloring problem. Graph 3 coloring problem is the problem faced during the color of the graph. To avoid this problem, color every vertex, edge and face of the graph with the three colors mention above.
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.