On leaky forcing and resilience

A leak is a vertex that not allowed to perform force during the zero forcing process. Leaky was recently introduced as new variation of in order analyze how leaks network disrupt The ?-leaky number graph size smallest set can despite ? leaks. G ?-resilient if its same number. In this paper, we and show an (??1)-leaky B robust enough, then set. This provides framework for characterizing sets. Furthermore, consider structural implications graphs. We apply these results bound several families including trees, supertriangles, grid particular, resolve question posed by Dillman Kenter concerning upper on 1-leaky