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

Row, Darren

doi:10.2140/involve.2011.4.277

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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

DOI: 10.2140/involve.2011.4.277

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. 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.)

Keywords

zero forcing number, path cover number, maximum nullity, cut-edge, cut-vertex, cactus

Mathematical Subject Classification 2010

Primary: 05C50

Secondary: 15A03

Milestones

Received: 5 May 2011

Revised: 12 May 2011

Accepted: 13 May 2011

Published: 13 March 2012

Communicated by Chi-Kwong Li

Authors

Darren D. Row
Division of Science and Mathematics Upper Iowa University Fayette, IA 52142 United States

Vol. 4, No. 3, 2011