An Approach for Solving the Graph Coloring Problem using Adjacency Matrix

Abstract

Coloring a graph is a known and a classical problem in graph theory. It is also a known NP problem. In a graph G, the solution of coloring a graph is about coloring all the vertices of the graph G in such a manner so that any two adjacent vertices do not get the similar color. This problem also requires that the number of colors that are used for coloring the graph are also minimum. There are several ways in which a graph can be presented. For example an adjacency matrix. In our paper we have used adjacency matrix to showcase the graph coloring solution. An adjacency matrix is a 2 dimensional array. The rows and columns of this array are therefore can also be called as the vertices of the graph. The value 0 indicates that the vertex on × row and y column is not connected. However if the value is 1 it indicates that the vertex on × row and y column are connected to each other. We have proposed an algorithm using which we calculate the diagonal values that is for which × row and y column value is same. These will represent the final colors allocated to the vertices.