The Zero Forcing Number of Twisted Hypercubes
Abstract
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≥ 3 with zero forcing sets of size 2k-1-2k-3+1, which is below the minimum zero forcing number of the hypercube.
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