arXiv:2611.13244v1 Announce Type: new Abstract: We show that the zero forcing number of the generalized Petersen graph $P(n,k)$ is $2k+2$ whenever $n\ge 2k^2+k+1$. We prove this by showing that the zero forcing number of the infinite generalized Petersen graph $P(\infty,k)$ is $2k+2$ and bounding the width of the closure of every set of at most $2k+1$ vertices. This bound gives a threshold on $n$ beyond which the projection of such a closure onto $P(n,k)$ does not wrap around. Combined with an exhaustive computer search for smaller $n$, we determine the zero forcing number of every $P(n,k)$ for $k\le 5$.
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