%0 Journal Article %T N-Set Distance-Labelings for Cycle Graphs %A Alissa Shen %A Jian Shen %J Open Journal of Discrete Mathematics %P 64-77 %@ 2161-7643 %D 2022 %I Scientific Research Publishing %R 10.4236/ojdm.2022.123005 %X Let G = (V, E) be a graph and C_m be the cycle graph with m vertices. In this paper, we continued Yeh＊s work [1] on the distance labeling of the cycle graph C_m. An n-set distance labeling of a graph G is the labeling of the vertices (with n labels per vertex) of G under certain constraints depending on the distance between each pair of the vertices in G. Following Yeh＊s notation [1], the smallest value for the largest label in an n-set distance labeling of G is denoted by 竹₁⁽ⁿ⁾(G). Basic results were presented in [1] for 竹₁⁽²⁾(C_m) for all m and 竹₁⁽ⁿ⁾(C_m) for some m where n ≡ 3. However, there were still gaps left unstudied due to case-by-case complexities. For these uncovered cases, we proved a lower bound for 竹