Matchstick graph

3-regular girth-5 matchstick graph
3-regular girth-5 matchstick graph
Vertices	54
Edges	81
Girth	5
	Table of graphs and parameters

Harborth graph
Harborth graph
Vertices	52
Edges	104
Radius	6
Diameter	9
Girth	3
	Table of graphs and parameters

In geometric graph theory, a branch of mathematics, a matchstick graph is a graph that can be drawn in the plane in such a way that its edges are line segments with length one that do not cross each other. That is, it is a graph that has an embedding which is simultaneously a unit distance graph and a plane graph. For this reason, matchstick graphs have also been called planar unit-distance graphs.^[1] Informally, matchstick graphs can be made by placing noncrossing matchsticks on a flat surface, hence the name.^[2]

^ Gervacio, Severino V.; Lim, Yvette F.; Maehara, Hiroshi (2008), "Planar unit-distance graphs having planar unit-distance complement", Discrete Mathematics, 308 (10): 1973–1984, doi:10.1016/j.disc.2007.04.050, MR 2394465
^ Weisstein, Eric W., "Matchstick graph", MathWorld{{cite web}}: CS1 maint: overridden setting (link)

[1] Gervacio, Severino V.; Lim, Yvette F.; Maehara, Hiroshi (2008), "Planar unit-distance graphs having planar unit-distance complement", Discrete Mathematics, 308 (10): 1973–1984, doi:10.1016/j.disc.2007.04.050, MR 2394465

[mmg-2] Weisstein, Eric W., "Matchstick graph", MathWorld{{cite web}}: CS1 maint: overridden setting (link)

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