Minimum rank and zero forcing number for butterfly networks
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Zero forcing is a graph propagation process introduced in quantum physics and theoretical computer science, and closely related to the minimum rank problem. The minimum rank of a graph is the smallest possible rank over all matrices described by a given network. We use this relationship to determine the minimum rank and the zero forcing number of butterfly networks, concluding they present optimal properties in regards to both problems.
KeywordsZero forcing Minimum rank of graphs Butterfly network
Mathematics Subject Classification05C96 05C57 94C15
We would like to thank an anonymous reviewer for carefully reading a previous version of the paper and providing a large number of insightful comments which were incredibly helpful in clarifying the presentation of our arguments.
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