Abstract
In this article an algorithm is presented for edges coloring of the graph. In this algorithm the node that we discuss represented by an Agent and then all the nodes of a graph like multi-agent system. Each node independently colours its edges with respect to cellular automata using distributed and paralleling of the process. Innovation of this method is on distributing of the process for each node so that each node updates its edges color only with the use of its neighbors in some steps until all graphs are colored completely. At the end the results are being tested on some Standard graphs and the results are presented. In this method, each graph is colored using one rule repetition for each node with high speed on its edges.