标题： 扭曲超立方体的零强迫数 显示英文标题

标题： The Zero Forcing Number of Twisted Hypercubes

摘要： 扭曲超立方体是通过放松对称性约束但保持度正则性和连通性来推广超立方体结构的图。我们研究了扭曲超立方体的零强迫数。 零强迫是一种图感染过程，在这个过程中，一个特定的颜色变化规则被迭代地应用于图和初始顶点集。 我们使用强迫弧集的替代框架构建了一组维度为 k$\geq 3$的扭曲超立方体，其零强迫集大小为$2^{k-1}-2^{k-3}+1$，这低于超立方体的最小零强迫数。 显示英文摘要

摘要： Twisted hypercubes are graphs that generalize the structure of the hypercube by relaxing the symmetry constraint while maintaining degree-regularity and connectivity. We study the zero forcing number of twisted hypercubes. Zero forcing is a graph infection process in which a particular colour change rule is iteratively applied to the graph and an initial set of vertices. We use the alternative framing of forcing arc sets to construct a family of twisted hypercubes of dimension k$\geq 3$ with zero forcing sets of size $2^{k-1}-2^{k-3}+1$, which is below the minimum zero forcing number of the hypercube.