棱柱图的精确支配：通过循环词按同余类进行枚举
Exact Dominion of the Prism Graph: Enumeration by Congruence Class via Cyclic Words
AI总结：
该研究通过循环词方法，提出了一种按同余类分层计算棱柱图支配数的显式公式，并揭示了支配问题在不同算术领域的特性。
摘要：
令G_n = C_n square P_2表示一个有2n个顶点的棱柱（圆梯形）图。通过将列配置编码为循环词，支配问题被转化为相邻因子上的局部布尔约束。该框架给出了支配ζ(G_n)的显式公式，按n mod 4进行分层，其中n属于{3, 6}的特殊情况通过计算验证。结合已知的支配数γ(G_n)，这些结果揭示了支配最优性的不同算术领域，从刚性强制到显著的枚举灵活性，并激发了用于评估参数图族结构韧性量化的定量参数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
