Vol. 4, No. 3, 2011

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Zero forcing number, path cover number, and maximum nullity of cacti

Darren D. Row

Vol. 4 (2011), No. 3, 277–291

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. The path cover number of a graph is the minimum size of a path cover. Results for comparing the parameters are presented, with equality of zero forcing number and path cover number shown for all cacti and equality of zero forcing number and maximum nullity for a subset of cacti. (A cactus is a graph where each edge is in at most one cycle.)

zero forcing number, path cover number, maximum nullity, cut-edge, cut-vertex, cactus
Mathematical Subject Classification 2010
Primary: 05C50
Secondary: 15A03
Received: 5 May 2011
Revised: 12 May 2011
Accepted: 13 May 2011
Published: 13 March 2012

Communicated by Chi-Kwong Li
Darren D. Row
Division of Science and Mathematics
Upper Iowa University
Fayette, IA 52142
United States