Unit distance graphs / Matchstick graphs
A catalog of 3-regular matchstick graphs of girth 5 consisting of 54 – 68 vertices (2019)
A 3-regular matchstick graph of girth 5 consisting of 54 vertices (2019)
Geombinatorics Quarterly, Volume XXIX, Issue 3, January 2020, Pages 116–121
4-regular planar unit triangle graphs without additional triangles (2019)
Geombinatorics Quarterly, Volume XXIX, Issue 2, October 2019, Pages 72–77
A catalogue of 4-regular and (2; 4)-regular matchstick graphs (2017)
On the existence of 4-regular matchstick graphs (2017)
Minimal completely asymmetric (4; n)-regular matchstick graphs (2016)
New minimal (4; n)-regular matchstick graphs (2016)
Geombinatorics Quarterly, Volume XXVII, Issue 1, July 2017, Pages 26–44
Ein neuer 4-regulärer Streichholzgraph (2016)
Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV), Band 24, Heft 2, Juli 2016, Seiten 74–75
Matchstick Graphs Calculator (MGC) – a software for the construction and calculation of unit distance graphs and matchstick graphs (2016–2019).
The graphs from the articles can be viewed with the MGC, which contains also a constructive proof for each graph. This remarkable software created by Stefan Vogel runs directly in web browsers. The method Stefan Vogel used for the calculations he describes in the article: Beweglichkeit eines Streichholzgraphen bestimmen.