A technique for computing the zero forcing number of a graph with a cut-vertex

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Abstract

The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. Results for determining graphs with extreme zero forcing numbers, for determining the zero forcing number of graphs with a cut-vertex, and for determining the zero forcing number of unicyclic graphs are presented.

AMS classification

05C50
15A03

Keywords

Zero forcing number
Zero spread
Maximum nullity
Cut-vertex reduction
Unicyclic graphs

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