Campus Units
Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
6-15-2012
Journal or Book Title
Linear Algebra and its Applications
Volume
436
Issue
12
First Page
4352
Last Page
4372
DOI
10.1016/j.laa.2010.10.015
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier Inc.
Copyright Date
2010
Language
en
File Format
application/pdf
Recommended Citation
Edholm, Christina J.; Hogben, Leslie; Huynh, My; LaGrange, Josh; and Row, Darren D., "Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph" (2012). Mathematics Publications. 211.
https://lib.dr.iastate.edu/math_pubs/211
Comments
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.