In this paper we study the homotopy type of Hom(Cm,Cn), where Ck is the cyclic graph with k vertices. We enumerate connected components of Hom(Cm,Cn) and show that each such component is either homeomorphic to a point or homotopy equivalent to S1. Moreover, we prove that Hom(Cm,Ln) is either empty or is homotopy equivalent to the union of two points, where Ln is an n-string, i.e., a tree with n vertices and no branching point
