6 citations · 14 across the 14 of their papers we have counts for
9 papers · 1 filter
Orthogonalisability of joins of graphs
Rupert H. Levene, Polona Oblak, Helena Šmigoc
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some…
Symmetric Nonnegative Trifactorization of Pattern Matrices
Damjana Kokol Bukovšek, Helena Šmigoc
A factorization of an nonnegative symmetric matrix of the form , where is a symmetric matrix, and both and are required to be nonne…
Powers of Karpelevic arcs and their Sparsest Realising matrices
Priyanka Joshi, Stephen Kirkland, Helena Smigoc
The region in the complex plane containing the eigenvalues of all stochastic matrices of order n was described by Karpelevic in 1988, and it is since then known as the Karpelevic r…
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
Aida Abiad, Shaun M. Fallat, Mark Kempton +5
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the j…
The liberation set in the inverse eigenvalue problem of a graph
Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc
The inverse eigenvalue problem of a graph is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the a…
Spectral arbitrariness for trees fails spectacularly
Shaun M. Fallat, H. Tracy Hall, Rupert H. Levene +4
If is a graph and is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph , what can we say about the eigenvalues of all…
Orthogonal symmetric matrices and joins of graphs
Rupert H. Levene, Polona Oblak, Helena Šmigoc
We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary condition for the join of two (possibly disconnected) graphs and to be the…
On the inverse eigenvalue problem for block graphs
Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc
The inverse eigenvalue problem of a graph aims to find all possible spectra for matrices whose -entry, for , is nonzero precisely when is adjacent to . I…
The strong spectral property for graphs
Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc
We introduce the set of all simple graphs with the property that each symmetric matrix corresponding to a graph has the st…