The NNN-Property of Cyclic Groups
Michael Giudici, Luke Morgan, Yian Xu
TL;DR
This paper investigates the NNN-property of cyclic groups within Cayley graphs, establishing that cyclic groups do not possess this property, thereby clarifying their structural characteristics in graph theory.
Contribution
The paper proves that cyclic groups lack the NNN-property, providing new insights into the structure of Cayley graphs associated with cyclic groups.
Findings
Cyclic groups do not have the NNN-property.
The study clarifies the structure of Cayley graphs for cyclic groups.
It distinguishes cyclic groups from other groups with the NNN-property.
Abstract
A Cayley graph is said to be an NNN-graph if it is both normal and non-normal for isomorphic regular groups, and a group has the NNN-property if there exists an NNN-graph for it. In this paper we investigate the NNN-property of cyclic groups, and show that cyclic groups do not have the NNN-property.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Topics in Algebra