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Matchstick graph - Wikipedia

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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] Much of the research on matchstick graphs has concerned regular graphs, in which each vertex has the same number of neighbors. This number is called the degree of the graph. Regular matchstick graphs can have degree 0, 1, 2, 3, or 4. The complete graphs with one, two, and three vertices (a single vertex, a single edge, and a triangle) are all matchstick graphs and are 0-, 1-, and 2-regular respectively. The smallest 3-regular matchstick graph is formed from two copies of the

Matchstick graph - Wikipedia Jump to content From Wikipedia, the free encyclopedia Graph with edges of length one, able to be drawn without crossings The unique smallest cubic matchstick graph Harborth graph Vertices 52 Edges 104 Radius 6 Diameter 9 Girth 3 Table of graphs and parameters 3-regular girth-5 matchstick graph Vertices 54 Edges 81 Girth 5 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,

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