Upper bound for the (d-2)-leaky forcing number of Q_d and ℓ-leaky forcing number of GP(n,1)

2022/02/25 by Herrman, Rebekah
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.12671

Abstract

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 at most 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.

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