In 2002, Hackmann and et al., introduced the concept of [r, s, t]-coloring . In fact in an [r,s,t]-coloring the difference between the colors of of every two adjacent vertices is more than r, between the colors of two adjacent edges is more than s and the difference between the colors of one vertex and its incident edges is more than t. The [r,s,t]-chromatic number of G is the minimum k such that G admits an[r,s,t]-coloring with k colors. Chapter one contains the fundamental necessary definition and the history of the concept. In chapter two, the general bounds for [r,s,t]-chromatic number are given.In chapter three the exact value or bounds of the [r,s,t]-chromatic number of stars, are given. In chapter four, we characterize some properties.