Let G_n = C_n square P_2 denote the prism (circular ladder) graph on 2n vertices. By encoding column configurations as cyclic words, domination is reduced to local Boolean constraints on adjacent factors. This framework yields explicit formulas for the dominion zeta(G_n), stratified by n mod 4, with the exceptional cases n in {3, 6} confirmed computationally. Together with the known domination numbers gamma(G_n), these results expose distinct arithmetic regimes governing optimal domination, ranging from rigid forcing to substantial enumerative flexibility, and motivate quantitative parameters for assessing structural robustness in parametric graph families.

翻译：设G_n = C_n □ P_2表示具有2n个顶点的棱柱（圆形阶梯）图。通过将列构型编码为循环字，支配问题被简化为相邻因子上的局部布尔约束。该框架给出了支配数zeta(G_n)的显式公式，并按n模4进行分层，其中例外情形n ∈ {3, 6}已通过计算验证。结合已知的支配数gamma(G_n)，这些结果揭示了支配最优化的不同算术机制，范围从刚性强制到显著的枚举灵活性，并为评估参数化图族的结构鲁棒性提供了量化参数。