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arXiv · 1711.00374

Graph classes for critical ideals, minimum rank and zero forcing number

Carlos A. Alfaro
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Abstract

Recently, there have been found new relations between the zero forcing number and the minimum rank of a graph with the algebraic co-rank. We continue on this direction by giving a characterization of the graphs with real algebraic co-rank at most 2. This implies that for any graph with at most minimum rank at most 3, its minimum rank is bounded from above by its real algebraic co-rank.

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Carlos A. Alfaro. 2017-10-31. Graph classes for critical ideals, minimum rank and zero forcing number. https://doi.org/10.1016/j.laa.2018.07.002

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