The (d−2)-leaky forcing number of Qd and ℓ-leaky forcing number of GP(n,1),Discrete Optimization

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The (d−2)-leaky forcing number of Qd and ℓ-leaky forcing number of GP(n,1)
Discrete Optimization ( IF 1.1 ) Pub Date : 2022-10-22 , DOI: 10.1016/j.disopt.2022.100744
Rebekah Herrman

Leaky-forcing is a recently introduced variant of zero forcing that has been studied for families of graphs including paths, cycles, wheels, grids, and trees. In this paper, we extend previous results on the leaky forcing number of the $d$ -dimensional hypercube, $Q_{d}$ , to show that the $(d - 2)$ -leaky forcing number of $Q_{d}$ is $2^{d - 1}$ . We also examine a question about the relationship between the size of a minimum $ℓ$ -leaky-forcing set and a minimum zero forcing set for a graph $G$ .

更新日期：2022-10-23

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