2024/03/06 by Bryan Curtis, Curtis, Bryan A., Leslie Hogben +3 · 1 citation
Computer Science · #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2403.03921
openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ZIR(G) and zir(G) are defined. Bounds on ZIR(G) and zir(G) are established and graphs having extreme values of ZIR(G) and 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.