Coloring Fuzzy Graphs and Traffic Light Problem


Authors

Siamak Firouzian - Department of Mathematics, Payame Noor University (PNU) Babol, Iran Mostafa Nouri Jouybari - Department of Mathematics, Payame Noor University (PNU) Babolsar, Iran


Abstract

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., \(C(i) \neq C(j)\). 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.


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ISRP Style

Siamak Firouzian, Mostafa Nouri Jouybari, Coloring Fuzzy Graphs and Traffic Light Problem, Journal of Mathematics and Computer Science, 2 (2011), no. 3, 431--435

AMA Style

Firouzian Siamak, Nouri Jouybari Mostafa, Coloring Fuzzy Graphs and Traffic Light Problem. J Math Comput SCI-JM. (2011); 2(3):431--435

Chicago/Turabian Style

Firouzian, Siamak, Nouri Jouybari, Mostafa. "Coloring Fuzzy Graphs and Traffic Light Problem." Journal of Mathematics and Computer Science, 2, no. 3 (2011): 431--435


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