Critical ideals, minimum rank and zero forcing number

Carlos A. Alfaro, Jephian C. -H. Lin

Published 2017-10-10Version 1

There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical ideal is trivial. This gives a new perspective for bounding and computing these three graph parameters.