Abstract: Discusses the edge coloring of two classes of graphs related to rirculant graphs. The following conclusions are obtained. (1) If G is a connected circulant graph with an odd prime power as its order, then G - v is Class 1 for any vertex v of G. (2) If G is a connected circulant graph of odd order, then the line graph L(G) of G is 1 -factorable if and only if the edge number of G is even.