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arXiv · 1607.07522

Minimum rank and zero forcing number for butterfly networks

Daniela Ferrero·Cyriac Grigorious·Thomas Kalinowski·Joe Ryan·Sudeep Stephen
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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 $\frac19\left[(3r+1)2^{r+1}-2(-1)^r\right]$ and that this is equal to the rank of its adjacency matrix.

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Daniela Ferrero, Cyriac Grigorious, Thomas Kalinowski, Joe Ryan, Sudeep Stephen. 2018-07-04. Minimum rank and zero forcing number for butterfly networks. https://doi.org/10.1007/s10878-018-0335-1

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