16 papers
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…
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…
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…
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…
Ramsey-type -bounds for -bounded graph classes
Tung Nguyen, Sang-il Oum
We prove that for every path , the class of graphs with no induced and no induced four-cycle is linearly -bounded. More generally, we ask for which pairs …
On -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…