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Descartes snark

From Wikipedia, the free encyclopedia
Descartes snark
Image of a Descartes snark.
Named afterBlanche Descartes
Vertices210
Edges315
Girth5
Chromatic index4
PropertiesCubic
Snark
Table of graphs and parameters

In the mathematical field of graph theory, a Descartes snark is an undirected graph with 210 vertices and 315 edges. It is a snark, first discovered by William Tutte in 1948 under the pseudonym Blanche Descartes.[1]

A Descartes snark is obtained from the Petersen graph by replacing each vertex with a nonagon and each edge with a particular graph closely related to the Petersen graph. Because there are multiple ways to perform this procedure, there are multiple Descartes snarks.

References

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  1. ^ Descartes, Blanche. "Network Colorings," The Mathematical Gazette (London, 32:299. p. 67–69, 1948.