Coloring Fuzzy Graphs and Traffic Light Problem

Given a graph?? = (??, ??), a coloring function ?? assigns an integer value ??(??) to each node ?????? in such a way that the extremes of any edge {??, ??}???? cannot share the same color, i.e., ??(??) ? ??(??). The classical concept of the (crisp) chromatic number of a graph ?? is generalized to fuzzy concept ?? in this paper. Main approach is based on the successive coloring functions ?? ?? of the crisp graphs the traffic lights problem is analyzed following this approach.