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.
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Taxonomy
TopicsFinite Group Theory Research · Limits and Structures in Graph Theory · graph theory and CDMA systems