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arXiv · 2505.01872

The Zero Forcing Number of Twisted Hypercubes

Peter Collier·Jeannette Janssen
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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$\geq 3$ with zero forcing sets of size $2^{k-1}-2^{k-3}+1$, which is below the minimum zero forcing number of the hypercube.

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Peter Collier, Jeannette Janssen. 2025-05-03. The Zero Forcing Number of Twisted Hypercubes. https://arxiv.org/abs/2505.01872

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