TL;DR
This paper catalogs all planar unit-distance matchstick graphs with up to 9 edges, revealing their classification by homeomorphism and isomorphism, and highlights the exponential growth in their quantities as edges increase.
Contribution
It provides a comprehensive classification of matchstick graphs with up to 9 edges, including counts of nonisomorphic and topologically distinct graphs, and discusses their rapid growth.
Findings
633 nonisomorphic connected matchstick graphs with 9 edges
196 topologically distinct graphs with 9 edges
Exponential increase in graph quantities with more edges
Abstract
Classification of planar unit-distance graphs with up to 9 edges, by homeomorphism and isomorphism classes. With exactly nine edges, there are 633 nonisomorphic connected matchstick graphs, of which 196 are topologically distinct from each other. Increasing edges' number, their quantities rise more than exponentially, in a still unclear way.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Graph Labeling and Dimension Problems