Abstarct: In this thesis first are explained the concept of color and color space and then fuzzy color model has been described. The proposed method defines a set of fuzzy colors baxsed on the HLS color space. Then, a fuzzy similarity measure is developed for evaluating the similarity of fuzzy colors. Also, is presented a fuzzy color clustering algorithm that is baxsed on a measure of similarity. This measure of color similarity is defined on a perceptual color system called HSL. In this thesis coloring of graphs using the concept of fuzzy color is shown and chromatic fuzzy sum and strength of fuzzy graph has been studied too.