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]
