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| volume = 47
| year = 2011| doi-access = free
}}. For additional details see the earlier preprint in {{cite
Every 4-regular matchstick graph contains at least 20 vertices.<ref name="Kurz,Pinchasi,2011">{{citation
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==Combinatorial enumeration==
The numbers of distinct (nonisomorphic) matchstick graphs are known for 1, 2, 3, ... up to ten edges; they are:
:1, 1, 3, 5, 12, 28, 74, 207, 633, 2008 {{OEIS|A066951}}<ref>{{cite
| last = Salvia | first = Raffaele
| year = 2013
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