2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72078In this paper we study the homotopy type of $\Hom(C_m,C_n)$, where $C_k$ is the cyclic graph with $k$ vertices. We enumerate connected components of $\Hom(C_m,C_n)$ and show that each such component is either homeomorphic to a point or homotopy equivalent to $S^1$. Moreover, we prove that $\Hom(C_m,L_n)$ is either empty or is homotopy equivalent to the union of two points, where $L_n$ is an $n$-string, i.e., a tree with $n$ vertices and no branching points.15 pages, 8 figures; Final version, to appear in Journal of Discrete and Computational GeometryCombinatorics05C15; 57M15text