Michael Tait

activity

20242026

collaborators

7 papers

math.CO2026

Connected graphs with minimum adjacency spectral gap

Lele Liu, Michael Tait, Yi Wang

Let $G$ be a connected graph, and let $λ_{1} (G) > λ_{2} (G)$ denote its two largest adjacency eigenvalues. The spectral gap of $G$ is defined as the difference $λ_{1} (G) - λ_{2} (G)$ . For in…

math.CO2026

Maximum spectral sum of graphs

Hitesh Kumar, Lele Liu, Hermie Monterde +2

For a graph $G$ of order $n$ , the spectral sum of $G$ is defined to be the sum $λ_{1} (G) + λ_{2} (G)$ , where $λ_{1} (G)$ (resp. $λ_{2} (G)$ ) is the largest (resp. second largest) adjacency ei…

math.CO2025

Cardinalities of $g$ -difference sets

Eric Schmutz, Michael Tait

Let $η_{g} (n)$ be the smallest cardinality that $A \subseteq Z$ can have if $A$ is a $g$ -difference basis for $[n]$ (i.e, if, for each $x \in [n]$ , there are {\em at least…

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.CO2024

Turán numbers for non-bipartite graphs and applications to spectral extremal problems

Longfei Fang, Michael Tait, Mingqing Zhai

Given a graph family $H$ with $min_{H \in H} χ (H) = r + 1 \geq 3$ . Let $ex (n, H)$ and $spex (n, H)$ be the maximum number of edges and th…

math.CO2024

Hypergraphs of girth 5 and 6 and coding theory

Kathryn Haymaker, Michael Tait, Craig Timmons

In this paper, we study the maximum number of edges in an $N$ -vertex $r$ -uniform hypergraph with girth $g$ where $g \in {5, 6}$ . Writing $ex_{r} (N, C_{< g})$ f…

math.CO2024

A general theorem in spectral extremal graph theory

John Byrne, Dheer Noal Desai, Michael Tait

The extremal graphs $EX (n, F)$ and spectral extremal graphs $SPEX (n, F)$ are the sets of graphs on $n$ vertices with maximum number of edges and m…

Connected graphs with minimum adjacency spectral gap

Maximum spectral sum of graphs

Cardinalities of g-difference sets

Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues

Turán numbers for non-bipartite graphs and applications to spectral extremal problems

Hypergraphs of girth 5 and 6 and coding theory

A general theorem in spectral extremal graph theory

Cardinalities of $g$ -difference sets