Vertex Partitions Based Approach to Solve the Graph Colouring Problem

The graph colouring problem is a NP- class problem explored in the literature due to its numerous applications in real world Engineering problems. Graph colouring problem involves to assign colours in such a fashion that neighbouring nodes have distinct colours. In this paper our objective is to find the number of distinct colours that can be used to colour the vertices in the graph. During the colouring process the objective is to use the least number of colours corresponding to considered graph. In this work we devise a new colouring algorithm using greedy technique by exploring the adjacent vertices which is simple and effective and can be used to compute the graph colouring problem in more enhanced way. The algorithm starts with the calculation of links of each vertex in the graph and then unexplored highest degree vertex will be selected for computation of adjacent nodes for colouring. Finally, we examined the presented algorithm on standard DIMACS graph colouring instances to evaluate the success of the devised algorithm. The result obtained after running the proposed algorithm for several categories of graphs like myciel, mugg, mulsol, david, huck, jean in terms of number of colours is equal to the chromatic number of the graph instances.