Campus Units
Mathematics
Document Type
Article
Publication Version
Published Version
Publication Date
1-2012
Journal or Book Title
Electronic Journal of Linear Algebra
Volume
23
First Page
79
Last Page
87
DOI
10.13001/1081-3810.1506
Abstract
The maximum positive semidefinite nullity of a multigraph G is the largest possible nullity over all real positive semidefinite matrices whose (i, j)th entry (for i not equal j) is zero if i and j are not adjacent in G, is nonzero if {i, j} is a single edge, and is any real number if {i, j} is a multiple edge. The definition of the positive semidefinite zero forcing number for simple graphs is extended to multigraphs; as for simple graphs, this parameter bounds the maximum positive semidefinite nullity from above. The tree cover number T(G) is the minimum number of vertex disjoint induced simple trees that cover all of the vertices of G. The result that M+ (G) = T(G) for an outerplanar multigraph G [F. Barioli et al. Minimum semidefinite rank of outerplanar graphs and the tree cover number. Electron. J. Linear Algebra, 22:10-21, 2011.] is extended to show that Z(+) (G) = M+ (G) = T(G) for a multigraph G of tree-width at most 2.
Copyright Owner
The Author(s)
Copyright Date
2012
Language
en
File Format
application/pdf
Recommended Citation
Ekstrand, Jason; Erickson, Craig; Hay, Diana; Hogben, Leslie; and Roat, Jolie, "Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees" (2012). Mathematics Publications. 251.
https://lib.dr.iastate.edu/math_pubs/251
Comments
This article is published as Ekstrand, Jason, Craig Erickson, Diana Hay, Leslie Hogben, and Jolie Roat. "Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees." The Electronic Journal of Linear Algebra 23 (2012): 79-87. DOI: 10.13001/1081-3810.1506. Posted with permission.