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the Grötzsch graph is the smallest triangle-free graph with its chromatic number.

Properties

The full automorphism group of the Grötzsch graph is isomorphic to the dihedral group D₅ of order 10, the group of symmetries of a regular pentagon, including both rotations and reflections. These symmetries have three orbits of vertices: the degree-5 vertex (by itself), its five neighbors, and its

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