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arXiv · 2403.03921

Zero forcing irredundant sets

Bryan A. Curtis·Leslie Hogben·Adriana Roux
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Abstract

Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined. Bounds on $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are established and graphs having extreme values of $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are characterized. The effect of the join and corona operations is studied. As the concept of a zero forcing irrdedundant set is new, there are many questions for future research.

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Bryan A. Curtis, Leslie Hogben, Adriana Roux. 2026-03-30. Zero forcing irredundant sets. https://arxiv.org/abs/2403.03921

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