Minimum rank and zero forcing number for butterfly networks

Abstract

The minimum rank of a simple graph $G$ is the smallest possible rank over all symmetric real matrices $A$ whose nonzero off-diagonal entries correspond to the edges of $G$. Using the zero forcing number, we prove that the minimum rank of the butterfly network is $\frac{1}{9}\left[(3r+1)2^{r+1}-2(-1{)}^r\right]$ and that this is equal to the rank of its adjacency matrix.

References in corpus (5)

• Full control by locally induced relaxation
• Propagation time for zero forcing on a graph
• Nondiscriminatory Propagation on Trees
• Power domination and zero forcing
• Power propagation time and lower bounds for power domination number

Cited by in corpus (1)

• Edge Forcing in Butterfly Networks