Tung T. Nguyen

activity

20222026

collaborators

17 papers

math.CO2026

Sedentariness in Cayley graphs

Karen Meagher, Hermie Monterde, Tung T. Nguyen

Let $A$ be the adjacency matrix of a finite graph $Γ$ . We say that vertex $u$ of $Γ$ is sedentary if for some constant $C > 0$ , $∣ exp (i t A)_{u, u} ∣ \geq C$ for all $t \in R$ . In…

math.RA2026

Sums of units in finite rings and applications to Cayley graphs

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

The question of whether a ring is additively generated by its units has been studied from several perspectives in ring theory and algebraic graph theory. In this paper, we investig…

math.NT2026

Cyclotomic factors of rational necklace functions

Nguyen Cao Minh, Nguyen Vu Hoang Minh, Dung Nguyen +3

Necklace polynomials arise in various fields of mathematics, including combinatorics, Lie theory, and Galois theory over finite fields. Their arithmetic properties have been extens…

math.CO2026

On gcd-graphs over matrix rings

Dung Nguyen, Tung T. Nguyen

Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number…

math.CO2026

Analytic Properties of Necklace Polynomials

Sunil K. Chebolu, Ján Mináč, Tung T. Nguyen +1

The necklace polynomials \[ M_n(x)=\frac1n\sum_{d\mid n}μ(d)x^{n/d} \] play a central role in discrete mathematics: they count aperiodic necklaces, enumerate monic irreducible poly…

math.CO2026

Ramsey-type $χ$ -bounds for $χ$ -bounded graph classes

Tung Nguyen, Sang-il Oum

We prove that for every path $P$ , the class of graphs with no induced $P$ and no induced four-cycle $C_{4}$ is linearly $χ$ -bounded. More generally, we ask for which pairs ${T, H}$ …

math.CO2026

On $U$ -unitary Cayley graphs over finite rings

Tung T. Nguyen, Nguyen Duy Tân

Graphs defined over a finite ring are well-studied in the literature. Due to their nature, these types of graphs connect several branches of mathematics, including algebra, number…

math.CO2025

On divisibility relation graphs

Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1

For each positive integer $n$ , we define the divisibility relation graph $D_{n}$ whose vertex set is the set of divisors of $n$ , and in which two vertices are adjacent if one is a di…

math.CO2025

Perfect state transfer on gcd-graphs over a finite Frobenius ring

Tung T. Nguyen, Nguyen Duy Tân

The existence of perfect state transfer (PST) on quantum spin networks is a fundamental problem in mathematics and physics. Various works in the literature have explored PST in gra…

math.NT2024

Isomorphic gcd-graphs over polynomial rings

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

Gcd-graphs over the ring of integers modulo $n$ are a simple and elegant class of integral graphs. The study of these graphs connects multiple areas of mathematics, including graph…

math.NT2024

Integral Cayley graphs over a finite symmetric algebra

Tung T. Nguyen, Nguyen Duy Tân

A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $…

math.CO2024

A complete classification of perfect unitary Cayley graphs

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of math…

math.NT2024

On the gcd graphs over polynomial rings

Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân

Gcd-graphs over the ring of integers modulo $n$ are a natural generalization of unitary Cayley graphs. The study of these graphs has foundations in various mathematical fields, inc…

math.CO2024

On certain properties of the $p$ -unitary Cayley graph over a finite ring

Tung T. Nguyen, Nguyen Duy Tân

In recent work, we study certain Cayley graphs associated with a finite commutative ring and their multiplicative subgroups. Among various results that we prove, we provide the nec…

math.RA2023

On the arithmetic of the join rings over finite fields

Sunil K. Chebolu, Jonathan Merzel, Ján Mináč +3

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…

math.RA2022

On the joins of group rings

Sunil K. Chebolu, Jonathan L. Merzel, Ján Mináč +4

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we define a subring of the ring $M_{n} (R)$ ( $n = \sum_{i = 1}^{d} ∣ G_{i} ∣)$ that encompasses all the individual group…

math.NT2022

Galois module structure of some elementary $p$ -abelian extensions

Lauren Heller, Jan Minac, Tung T. Nguyen +2

We determine the Galois module structure of the parameterizing space of elementary $p$ -abelian extensions of a field $K$ when $Gal (K / F)$ is any finite $p$ -group, under the a…

Sedentariness in Cayley graphs

Sums of units in finite rings and applications to Cayley graphs

Cyclotomic factors of rational necklace functions

On gcd-graphs over matrix rings

Analytic Properties of Necklace Polynomials

Ramsey-type χ-bounds for χ-bounded graph classes

On U-unitary Cayley graphs over finite rings

On divisibility relation graphs

Perfect state transfer on gcd-graphs over a finite Frobenius ring

Isomorphic gcd-graphs over polynomial rings

Integral Cayley graphs over a finite symmetric algebra

A complete classification of perfect unitary Cayley graphs

On the gcd graphs over polynomial rings

On certain properties of the p-unitary Cayley graph over a finite ring

On the arithmetic of the join rings over finite fields

On the joins of group rings

Galois module structure of some elementary p-abelian extensions

Ramsey-type $χ$ -bounds for $χ$ -bounded graph classes

On $U$ -unitary Cayley graphs over finite rings

On certain properties of the $p$ -unitary Cayley graph over a finite ring

Galois module structure of some elementary $p$ -abelian extensions