W. Barrett

activity

20062023

most citedSparsity of Graphs that Allow Two Distinct Eigenvalues

1 citations · 3 across the 9 of their papers we have counts for

collaborators

13 papers

math.CO2023★ 1 cited

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.CO2022

On the Laplacian spread of digraphs

Wayne Barrett, Thomas R. Cameron, Emily Evans +2

In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values f…

math.CO2022★ 1 cited

Sparsity of Graphs that Allow Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +5

The parameter $q (G)$ of a graph $G$ is the minimum number of distinct eigenvalues over the family of symmetric matrices described by $G$ . It is shown that the minimum number of edg…

math.CO2022

New conjectures on algebraic connectivity and the Laplacian spread of graphs

Wayne Barrett, Emily Evans, H. Tracy Hall +1

We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implie…

math.CO2019

Spanning 2-Forests and Resistance Distance in 2-Connected Graphs

Wayne Barrett, Emily J. Evans, Amanda E. Francis +2

A spanning 2-forest separating vertices $u$ and $v$ of an undirected connected graph is a spanning forest with 2 components such that $u$ and $v$ are in distinct components. Aside…

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…