University of Isfahan Transactions on Combinatorics 2251-8657 15 4 2025 11 20 Failed zero forcing numbers of grassmann graphs 295 304 30057 10.22108/toc.2025.145774.2295 EN Fatemeh Afzali Department of Mathematics, Faculty of Science Shahid Rajaee, Teacher Training University, Tehran, Iran Amir Hossein Ghodrati Department of Mathematics, Faculty of Science Shahid Rajaee, Teacher Training University, Tehran, Iran Hamid Reza Maimani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran. Journal Article 2025 06 29 For a graph $G$ with vertices colored either black or white, consider the following rule to change the colors: the color of a vertex which is the only white neighbor of a black vertex, changes from white to black. A proper subset $S$ of the vertex set of $G$ is called a failed zero forcing set if, regardless of how many times this rule is applied to a graph with the initial black vertices $S$, at least one white vertex always remains. The maximum size of such a subset is called the failed zero forcing number of $G$ and is denoted by $F(G)$. In this paper, we look at the failed zero forcing numbers of Grassmann graphs $J_q(n, 2)$ and prove that $F(J_q(n, 2))={n \brack 2}_q - b'_2(q)$, for $n\geq 5$, where $b'_2(q)$ is the maximum number of points in the affine or projective plane of order $q$ such that there is no line that passes through exactly one of these points. Moreover, using maximum arcs in the projective planes, we show that if $q$ is a power of two, then $F(J_q(n, 2))={n \brack 2}_q - (q + 2)$. https://toc.ui.ac.ir/article_30057_3a6bb0a913a680628dae5ffe471c1949.pdf