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papers

Publications (15)

math.CO2023

Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +3

For an $n \times n$ matrix $A$ , let $q (A)$ be the number of distinct eigenvalues of $A$ . If $G$ is a connected graph on $n$ vertices, let $S (G)$ be the set of all real sy…

math.CO2017

Resistance distance in straight linear 2-trees

Wayne Barrett, Emily J. Evans, Amanda E. Francis

We consider the graph $G_{n}$ with vertex set $V (G_{n}) = {1, 2, \dots, n}$ and ${i, j} \in E (G_{n})$ if and only if $0 < ∣ i - j ∣ \leq 2$ . We call $G_{n}$ the straight linear 2-tree on $n…

math.CO2008

The minimum rank problem over the finite field of order 2: minimum rank 3

Wayne Barrett, Jason Grout, Raphael Loewy

Our main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also l…

math.CO2017

The inverse eigenvalue problem of a graph: Multiplicities and minors

Wayne Barrett, Steve Butler, Shaun M. Fallat +5

The inverse eigenvalue problem of a given graph $G$ is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G…

math.CO2007

The inverse inertia problem for graphs

Wayne Barrett, H. Tracy Hall, Raphael Loewy

Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions correspond…

math.CO2016

Equitable Decompositions of Graphs

Wayne Barrett, Amanda Francis, Ben Webb

We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $I ¨ $ , it i…