PreprintCC BY 4.0arXiv
On gcd-graphs over matrix rings
Abstract
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 theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields. We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest.
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BibTeX
@misc{nguyen2026gcdgraphs,
title = {{On gcd-graphs over matrix rings}},
author = {Dung Nguyen and Tung T. Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.00836},
eprint = {2606.00836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00836},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On gcd-graphs over matrix rings
AU - Dung Nguyen
AU - Tung T. Nguyen
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2606.00836
UR - https://arxiv.org/abs/2606.00836
AB - 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 theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields. We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest.
ER -