Abstarct: Fuzzy-set theory was introduced by Zadeh in 1965. Usually, applied methods of modeling and designing a system need to complexes and advanced mathematics. These mathematics are expressed with expert acknowledge and linguistic variable. A lot of the ambiguity can be resolved in modeling by applying fuzzy concept on vertices and edges of graph. This study deals with fuzzy graph coloring. Given a graph G = (V; E), a coloring function C assigns an integer value C(i) to each node i ∈V in such a way that the extremes of any edge cannot share the same color, i.e., C(i) ≠ C(j). In this study during exxpression of fuzzy graph coloring, for partitioning of models that its partitions have decrees value is defined colors set close to 1 and with presentation sum coloring for fuzzy graph optimum fuzzy extended chromatic partition is expressed. Also application of this problem in exam scheduling that fuzzy color is slot value of exam. Calculation results on some random fuzzy graph are expressed for comparison. An interval coloring is expressed baxsed on edges intensity for weighted graph with crisp vertices and fuzzy edges and its application at traffic problem is presented. An exact algorithm for obtaining the chromatic number is proposed, and some computational results for test of algorithm on randomly generated fuzzy graphs are reported. A circular coloring To get a better answer than a weighted fuzzy graph interval coloring is defined and a linear program to find the chromatic number and the corresponding function is provided.