Brendan Rooney

activity

20162026

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

1 citations · 2 across the 5 of their papers we have counts for

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6 papers · 1 filter

math.CO2024

Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues

Wayne Barrett, Shaun Fallat, Veronika Furst +3

The parameter $q (G)$ of an $n$ -vertex graph $G$ is the minimum number of distinct eigenvalues over the family of symmetric matrices described by $G$ . We show that all $G$ with $e(\…

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★ 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.CO2021

Efficient (j,k)-Domination in Regular Graphs

Brendan Rooney

Rubalcaba and Slater (Robert R. Rubalcaba and Peter J. Slater. Efficient (j,k)-domination. Discuss. Math. Graph Theory, 27(3):409-423, 2007.) define a $(j, k)$ -dominating function o…

math.CO2018

Vector Coloring the Categorical Product of Graphs

Chris Godsil, David E. Roberson, Brendan Rooney +2

A vector $t$ -coloring of a graph is an assignment of real vectors $p_{1}, \dots, p_{n}$ to its vertices such that $p_{i}^{T} p_{i} = t - 1$ for all $i = 1, \dots, n$ and $p_{i}^{T} p_{j} \leq - 1$ whene…

math.CO2016

Graph Homomorphisms via Vector Colorings

Chris Godsil, David E. Roberson, Brendan Rooney +2

In this paper we study the existence of homomorphisms $G \to H$ using semidefinite programming. Specifically, we use the vector chromatic number of a graph, defined as the smallest…