# Coloring Fuzzy Graphs and Traffic Light Problem

Volume 2, Issue 3, pp 431--435
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### 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.

### Share and Cite

##### 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

### Keywords

• Fuzzy graph
• Coloring
• Traffic Light Problem.

•  05C72
•  05C15
•  90B20

### References

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