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

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