Minimal 3-regular Penny Graph
Alexander Karabegov, Tanya Khovanova

TL;DR
This paper proves that the smallest 3-regular penny graph has 16 vertices and constructs an example of such a graph, establishing the minimal size and existence.
Contribution
It establishes the minimal number of vertices in 3-regular penny graphs and provides an explicit example, advancing understanding of penny graph properties.
Findings
A 3-regular penny graph has at least 16 vertices.
An explicit 16-vertex 3-regular penny graph exists.
The minimal size for such graphs is exactly 16 vertices.
Abstract
We prove that a 3-regular penny graph has at least 16 vertices and show that such a graph with 16 vertices exists.
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 · Limits and Structures in Graph Theory · graph theory and CDMA systems
