1 citations · 2 across the 4 of their papers we have counts for
8 papers
Stochastic Matrices Realising the Boundary of the Karpelevi\v c Region
Stephen Kirkland, Helena Šmigoc
A celebrated result of Karpelevi\v c describes the collection of all eigenvalues arising from the stochastic matrices of order The boundary of consists of roots o…
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 Karpelevič Region Revisited
Stephen Kirkland, Thomas Laffey, Helena Smigoc
We consider the Karpelevič region consisting of all eigenvalues of all stochastic matrices of order . We provide an alternative characterisation of $Θ_n…
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…
A Nordhaus-Gaddum conjecture for the minimum number of distinct eigenvalues of a graph
Rupert H. Levene, Polona Oblak, Helena Šmigoc
We propose a Nordhaus-Gaddum conjecture for , the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph : for every graph excluding fou…