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arXiv · 2305.11748

The $Z_q$-forcing number for some graph families

Jorge Blanco·Stephanie Einstein·Caleb Hostetler·Jurgen Kritschgau·Daniel Ogbe
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Abstract

The zero forcing number was introduced as a combinatorial bound on the maximum nullity taken over the set of real symmetric matrices that respect the pattern of an underlying graph. The $Z_q$-forcing game is an analog to the standard zero forcing game which incorporates inertia restrictions on the set of matrices associated with a graph. This work proves an upper bound on the $Z_q$-forcing number for trees. Furthermore, we consider the $Z_q$-forcing number for caterpillar cycles on $n$ vertices. We focus on developing game theoretic proofs of upper and lower bounds.

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Jorge Blanco, Stephanie Einstein, Caleb Hostetler, Jurgen Kritschgau, Daniel Ogbe. 2023-05-19. The $Z_q$-forcing number for some graph families. https://arxiv.org/abs/2305.11748

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