8 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…
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…
Maximal -extensions of Pythagorean fields and Right Angled Artin Groups
Oussama Hamza, Christian Maire, Ján Mináč +1
In this paper, we describe minimal presentations of maximal pro- quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we int…
On divisibility relation graphs
Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1
For each positive integer , we define the divisibility relation graph whose vertex set is the set of divisors of , and in which two vertices are adjacent if one is a di…
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 $…
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…
On the strong Massey property for number fields
Christian Maire, Ján Mináč, Ravi Ramakrishna +1
Let . We show that for every number field with , the absolute and tame Galois groups of satisfy the strong -fold Massey property relative to .…
On the gcd graphs over polynomial rings
Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân
Gcd-graphs over the ring of integers modulo are a natural generalization of unitary Cayley graphs. The study of these graphs has foundations in various mathematical fields, inc…