David Dolžan

activity

20102026

most citedDiameters of commuting graphs of matrices over semirings

11 citations · 17 across the 15 of their papers we have counts for

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12 papers · 1 filter

math.RA2026

Products of Nilpotent and Idempotent Matrices over Finite Local Rings

David Dolžan

Let $R$ be a finite commutative local principal ring. We study products of nilpotent and idempotent matrices in $M_{2} (R)$ . We show that every product of nilpotent and idempotent mat…

math.RA2026

Eigenvalues of the product matrices of finite commutative rings

David Dolžan

The product matrix of a finite commutative ring $R = {x_{1}, x_{2}, \dots, x_{n}}$ and an element $u \in R$ is the matrix $A_{u} (R) = [a_{ij}]$ , where $a_{ij} = 1$ if $x_{i} x_{j} = u$ , and $a_{ij} = 0$ …

math.RA2025

Products of nilpotents in a quaternion ring of odd order

David Dolžan

Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ , where $q = p^{r}$ for an odd prime $p$ and integer $r$ with $R / J (R) ≃ GF (q)$ . We determine the number…

math.RA2025

Products of idempotents in a quaternion ring

David Dolžan

Let $R$ be a finite commutative local principal ring, and let $H (R)$ denote the corresponding quaternion ring. We show that an element of $H (R)$ is a product of idempotents if and…

math.RA2025

The multiplication probability of a finite ring

David Dolžan

We study the probability that the product of two randomly chosen elements in a finite ring $R$ is equal to some fixed element $x \in R$ . We calculate this probability for semisimpl…

math.RA2024

On the sumsets of exceptional units in quaternion rings

Hassan Cheraghpour, David Dolžan

We investigate sums of exceptional units in a quaternion ring $H (R)$ over a finite commutative ring $R$ . We prove that in order to find the number of representations of an element…

math.RA2024

The metric dimension of the total graph of a semiring

David Dolžan

We calculate the metric dimension of the total graph of a direct product of finite commutative antinegative semirings with their sets of zero-divisors closed under addition.

math.RA2024

Semirings generated by idempotents

David Dolžan

We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a…

math.RA2023

The unitary Cayley graph of a semiring

David Dolžan

We study the unitary Cayley graph of a matrix semiring. We find bounds for its diameter, clique number and independence number, and determine its girth. We also find the relationsh…

math.RA2021

The Metric Dimension of the Zero-Divisor Graph of a Matrix Semiring

David Dolžan

We determine the metric dimension of the zero-divisor graph of the matrix semiring over a commutative entire antinegative semiring.

math.RA2014

The total graphs of finite rings

David Dolžan, Polona Oblak

In this paper we extend the study of total graphs $τ (R)$ to non-commutative finite rings $R$ . We prove that $τ (R)$ is connected if and only if $R$ is not local and we see that in t…

math.RA2010★ 11 cited

Diameters of commuting graphs of matrices over semirings

David Dolžan, Damjana Kokol Bukovšek, Polona Oblak

We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the…