A Novel ABC Optimization Algorithm for Graph Coloring Problem

Abstract

In this paper, graph coloring has been done using artificial bee colony (ABC) optimization algorithm. Graph coloring deals with the challenge of coloring the nodes of any graph by least possible number of colors while ensuring on same time that two adjacent nodes does not gain same color. That least possible count of colors used denotes the chromatic number of a graph and to determine this number for any graph is an NP-complete problem hence no existing polynomial time algorithm can solve it. To find the best coloring sequence, a large search space has to be explored. Graph coloring deals with the challenge of coloring the nodes of any graph by least possible number of colors while ensuring on same time that two adjacent nodes does not gain same color and proposed a novel artificial bee colony (ABC) optimization algorithm for graph coloring. In this paper, we analyzed the proposed algorithm and compared it with three other graph coloring algorithms i.e. first fit, largest degree based ordering (LDO) and saturation degree based ordering (SDO). These results also indicate that ABC algorithm converges in a few iterations and is able to optimally allocate colors to vertices of a graph.