28 citations · 36 across the 13 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…