Chromatic number of fuzzy graphs
نویسنده
چکیده
Abstract. Coloring of fuzzy graphs plays a vital role in theory and practical applications. The concept of chromatic number of fuzzy graphs was introduced by Munoz[6] et.al. Later Eslahchi and Onagh [7]defined fuzzy coloring of fuzzy graphs and defined fuzzy chromatic number χ (G). Incorporating the features of these two definitions, the definition of chromatic number of a fuzzy graph χ(G), is modified in terms of chromatic number of threshold graph Gα and established that χ f (G) = χ(G). The advantage of this definition is that the chromatic number of a fuzzy graph can be obtained directly from the chromatic number of threshold graph Gα, which is a crisp graph. Also algorithms are proposed to find chromatic number of crisp graph and fuzzy graph. The solution for the banquet problem is found using the chromatic number of the corresponding fuzzy graph.
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