Coloring Fuzzy Graphs And Traffic Light Problem
Siamak Firouzian, Mostafa Nouri Jouybari · Journal of Mathematics and Computer Science · 2011
Given a graph \(G=(V,E)\), a coloring function \(C\) assigns an integer value \(C(i)\) to each node \(i\in V\) in such a way that the extremes of any edge \(\{i,j\}\in E\) cannot share the same color, i.e., \(C(i) eq C(j)\). The classical concept of the (crisp) chromatic number of a graph \(G\) is generalized to fuzzy concept \(\tilde{G}\) in this paper. Main approach is based on the successive coloring functions \(C_\alpha\) of the crisp graphs \(G_{\alpha}= (V; E_{\alpha})\), the \(\alpha\)−cuts of \(\tilde{G}\) ; the traffic lights problem is analyzed following this approach.