Shaun M. Fallat

activity

20132021

collaborators

8 papers

math.CO2021

On the minimum number of distinct eigenvalues of a threshold graph

Shaun Fallat, Seyed Ahmad Mojallal

For a graph $G$ , we associate a family of real symmetric matrices, $S (G)$ , where for any $A \in S (G)$ , the location of the nonzero off-diagonal entries of $A$ are governed by the ad…

math.CO2020

The Erdős-Ko-Rado theorem for $2$ -intersecting families of perfect matchings

Shaun Fallat, Karen Meagher, Mahsa N. Shirazi

A perfect matching in the complete graph on $2 k$ vertices is a set of edges such that no two edges have a vertex in common and every vertex is covered exactly once. Two perfect mat…

math.CO2020

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…

math.SP2019

Achievable multiplicity partitions in the inverse eigenvalue problem of a graph

Mohammad Adm, Shaun Fallat, Karen Meagher +3

Associated to a graph $G$ is a set $S (G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the gr…

math.CO2018

Properties of a $q$ -analogue of zero forcing

Steve Butler, Craig Erickson, Shaun Fallat +6

Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation…

math.CO2018

On the almost-principal minors of a symmetric matrix

Shaun M. Fallat, Xavier Martínez-Rivera

The almost-principal rank characteristic sequence (apr-sequence) of an $n \times n$ symmetric matrix is introduced, which is defined to be the string $a_{1} a_{2} \dots a_{n - 1}$ , where…