7 papers · 1 filter
Enumeration of Laplacian integral and {-1,0,1}-diagonalizable graphs
Nathaniel Johnston, Sarah Plosker, Luis M. B. Varona
A graph with Laplacian matrix is called Laplacian integral if the eigenvalues of are all integers, and it is called -diagonalizable if has a full set of eig…
The Factor Width Rank of a Matrix
Nathaniel Johnston, Shirin Moein, Sarah Plosker
A matrix is said to have factor width at most if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single principal submatri…
Laplacian - and -diagonalizable graphs
Nathaniel Johnston, Sarah Plosker
A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagona…
Weakly Hadamard diagonalizable graphs and Quantum State Transfer
Darian McLaren, Hermie Monterde, Sarah Plosker
Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of q…
Complex Hadamard Diagonalisable Graphs
Ada Chan, Shaun Fallat, Steve Kirkland +3
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex…
Centrosymmetric Stochastic Matrices
Lei Cao, Darian McLaren, Sarah Plosker
We consider the convex set of stochastic matrices and the convex set of centrosymmetric stochastic matrices (stochastic…