Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph

Date
2012-06-15
Authors
Edholm, Christina
Hogben, Leslie
Huynh, My
LaGrange, Josh
Row, Darren
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Abstract

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i not equal j) is nonzero whenever {i, j} is an edge in G and is zero otherwise; maximum nullity is taken over the same set of matrices. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. The spread of a graph parameter at a vertex v or edge e of G is the difference between the value of the parameter on G and on G - v or G - e. Rank spread (at a vertex) was introduced in [4]. This paper introduces vertex spread of the zero forcing number and edge spreads for minimum rank/maximum nullity and zero forcing number. Properties of the spreads are established and used to determine values of the minimum rank/maximum nullity and zero forcing number for various types of grids with a vertex or edge deleted.

Description

This is a manuscript of an article published as Edholm, Christina J., Leslie Hogben, My Huynh, Joshua LaGrange, and Darren D. Row. "Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph." Linear Algebra and its Applications 436, no. 12 (2012): 4352-4372. DOI: 10.1016/j.laa.2010.10.015. Posted with permission.

Keywords
zero spread, null spread, rank spread, zero forcing number, maximum nullity, minimum rank, supertriangle, grid graph, triangular grid, king grid
Citation
DOI
Collections