The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).
The circular chromatic number of a graph is a natural generalization of the chromatic number. Circular chromatic number contains more information about the structure of a graph than chromatic number does. In this paper we obtain the circular chromatic numbers of special graphs such as C t k and C t k-v, and give a simple proof of the circular chromatic number of H m,n .
