English

Zero forcing irredundant sets

Combinatorics 2026-03-31 v3

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 \mboxZIR(G)\mbox{ZIR}(G) and \mboxzir(G)\mbox{zir}(G) are defined. Bounds on \mboxZIR(G)\mbox{ZIR}(G) and \mboxzir(G)\mbox{zir}(G) are established and graphs having extreme values of \mboxZIR(G)\mbox{ZIR}(G) and \mboxzir(G)\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.

Keywords

Cite

@article{arxiv.2403.03921,
  title  = {Zero forcing irredundant sets},
  author = {Bryan A. Curtis and Leslie Hogben and Adriana Roux},
  journal= {arXiv preprint arXiv:2403.03921},
  year   = {2026}
}
R2 v1 2026-06-28T15:11:21.166Z