Minimum semidefinite rank of outerplanar graphs and the tree cover number

DOI10.13001/1081-3810.1424zbMath1205.05135OpenAlexW284370259MaRDI QIDQ3075196

Shaun M. Fallat, Sivaram K. Narayan, Francesco Barioli, Lon H. Mitchell

Publication date: 10 February 2011

Published in: The Electronic Journal of Linear Algebra (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/224678

zbMATH Keywords

outerplanar graphsminimum semidefinite rankmaximum multiplicitytree cover numberminimum rank graph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (14)

On the tree cover number of a graph ⋮ Positive Semidefinite Zero Forcing: Complexity and Lower Bounds ⋮ Vector representations of graphs and distinguishing quantum product states with one-way LOCC ⋮ An integer program for positive semidefinite zero forcing in graphs ⋮ Minimum rank of outerplanar graphs ⋮ Positive semidefinite zero forcing ⋮ Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs ⋮ A New Lower Bound for Positive Zero Forcing ⋮ Lower bounds for positive semidefinite zero forcing and their applications ⋮ On the relationships between zero forcing numbers and certain graph coverings ⋮ Positive semidefinite zero forcing numbers of two classes of graphs ⋮ Unnamed Item ⋮ More Applications of the $d$-Neighbor Equivalence: Acyclicity and Connectivity Constraints ⋮ Graph complement conjecture for classes of shadow graphs

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