On the $m$-graph of a finite Abelian Group
Abstract
Let $H$ be a finite abelian (commutative) group of order $n \geq 2$, and $m >1$ be an integer. We define the $m$-graph of $H$, denoted by $m-G(H)$, as a simple undirected graph with vertex set $H$, and two distinct vertices, $a, b \in H$, are connected by an edge if and only if $a^m = b$ or $b^m = a$. Several results regarding the properties of the $m$-$G(H)$ have been established.
Fields of Study & Subjects
Finite Group Theory Research
Graph theory and applications
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint