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Polyhedral 4-Vertex Graph

A polyhedral 4-vertex graph is a polyhedral graph on four vertices. Up to isomorphism, there is only one such graph, the tetrahedral graph, which is the complete graph K_4 (Duijvestijn and Federico 1981).

A polyhedral graph is 3-connected, so its minimum vertex degree is at least 3. On four vertices, each vertex must therefore be joined to all three others.

See also

Complete Graph, Polyhedral Graph, Tetrahedral Graph

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References

Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput. 37, 523-532, 1981. https://doi.org/10.1090/S0025-5718-1981-0628713-3.House of Graphs. Polyhedral 4-Vertex Graphs. Tetrahedron K_4.

Cite this as:

Weisstein, Eric W. "Polyhedral 4-Vertex Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Polyhedral4-VertexGraph.html

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