28 citations · 36 across the 13 of their papers we have counts for
16 papers
Gram mates, sign changes in singular values, and isomorphism
Sooyeong Kim, Steve Kirkland
We study distinct matrices and , called \textit{Gram mates}, such that and . We characterize Gram mates where one can be obtained from the oth…
Fiedler vectors with unbalanced sign patterns
Sooyeong Kim, Steve Kirkland
In spectral bisection, a Fielder vector is used for partitioning a graph into two connected subgraphs according to its sign pattern. In this article, we investigate graphs having F…
Numerical ranges of cyclic shift matrices
Mao-Ting Chien, Steve Kirkland, Chi-Kwong Li +1
We study the numerical range of an cyclic shift matrix, which can be viewed as the adjacency matrix of a directed cycle with weighted arcs. In particular, we consid…
Clusters in Markov Chains via Singular Vectors of Laplacian Matrices
Sam Cole, Steve Kirkland
Suppose that is a stochastic matrix. We propose an algorithm for identifying clusters in the Markov chain associated with . The algorithm is recursive in nature, and in orde…
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…
On Kemeny's constant for trees with fixed order and diameter
Lorenzo Ciardo, Geir Dahl, Steve Kirkland
Kemeny's constant of a connected graph is a measure of the expected transit time for the random walk associated with . In the current work, we consider the case when…
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…
The Complexity of Power Graphs Associated With Finite Groups
S. Kirkland, A. R. Moghaddamfar, S. Navid Salehy +2
The power graph of a finite group is the graph whose vertex set is , and two elements in are adjacent if one of them is a power of the other. The purpos…
Switching and partially switching the hypercube while maintaining perfect state transfer
Steve Kirkland, Sarah Plosker, Xiaohong Zhang
A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to P…
Perfect quantum state transfer in weighted paths with potentials (loops) using orthogonal polynomials
Steve Kirkland, Darian McLaren, Rajesh Pereira +2
A simple method for transmitting quantum states within a quantum computer is via a quantum spin chain---that is, a path on vertices. Unweighted paths are of limited use, and so…
Perfect quantum state transfer using Hadamard diagonalizable graphs
Nathaniel Johnston, Steve Kirkland, Sarah Plosker +2
Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the c…
Bounds on probability of state transfer with respect to readout time and edge weight
Whitney Gordon, Steve Kirkland, Chi-Kwong Li +2
We analyse the sensitivity of a spin chain modelled by an undirected weighted connected graph exhibiting perfect state transfer to small perturbations in readout time and edge weig…
On split graphs with four distinct eigenvalues
Felix Goldberg, Steve Kirkland, Anu Varghese +1
It is a well-known fact that a graph of diameter has at least eigenvalues. Let us call a graph \emph{-extremal} if it has diameter and exactly eigenvalues. S…
The Markov chain tree theorem and the state reduction algorithm in commutative semirings
Buket Benek Gursoy, Steve Kirkland, Oliver Mason +1
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal a…
On the sign patterns of the smallest signless Laplacian eigenvector
Felix Goldberg, Steve Kirkland
Let be a connected bipartite graph, whose signless Laplacian matrix is . Suppose that the bipartition of is and that is the eigenvector of the smallest ei…
On the Markov Chain Tree Theorem in the Max Algebra
Buket Benek Gursoy, Steve Kirkland, Oliver Mason +1
The Markov Chain Tree Theorem is extended to the max algebra and possible applications to ranking problems are discussed.