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.

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.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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