Regular matchstick graphs on the sphere
Konrad J. Swanepoel
TL;DR
This paper characterizes all 5-regular matchstick graphs on the sphere, proving they are precisely the five contact graphs of congruent caps identified by Robinson in 1969.
Contribution
It provides a complete classification of 5-regular matchstick graphs on the sphere, linking them to Robinson's contact graphs from 1969.
Findings
Exactly five 5-regular matchstick graphs on the sphere
These graphs correspond to Robinson's contact graphs of congruent caps
The classification confirms Robinson's earlier findings
Abstract
We show that the -regular matchstick graphs on the sphere are exactly the five -regular contact graphs of congruent caps on the sphere found by R. M. Robinson (1969).
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory