Title
A variant on the graph parameters of Colin de Verdière: Implications to the minimum rank of graphs
Campus Units
Mathematics
Document Type
Article
Publication Version
Published Version
Publication Date
12-2005
Journal or Book Title
Electronic Journal of Linear Algebra
Volume
13
First Page
387
Last Page
404
DOI
10.13001/1081-3810.1170
Abstract
For a given undirected graph G, the minimum rankof G is defined to be the smallest possible rank over all real symmetric matrices A whose (i, j)th entry is nonzero whenever i not equal j and {i, j} is an edge in G. Building upon recent work involving maximal coranks (or nullities) of certain symmetric matrices associated with a graph, a new parameter xi is introduced that is based on the corank of a different but related class of symmetric matrices. For this new parameter some properties analogous to the ones possessed by the existing parameters are verified. In addition, an attempt is made to apply these properties associated with xi to learn more about the minimum rankof graphs - the original motivation.
Copyright Owner
The Author(s)
Copyright Date
2005
Language
en
File Format
application/pdf
Recommended Citation
Barioli, Francesco; Fallat, Shaun; and Hogben, Leslie, "A variant on the graph parameters of Colin de Verdière: Implications to the minimum rank of graphs" (2005). Mathematics Publications. 257.
https://lib.dr.iastate.edu/math_pubs/257
Comments
This article is published as Barioli, Francesco, Shaun Fallat, and Leslie Hogben. "A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs." The Electronic Journal of Linear Algebra 13 (2005): 387-404. DOI: 10.13001/1081-3810.1170. Posted with permission.