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The Folkman graph is a semisymmetric graph that has the minimum possible number of nodes (20) (Skiena 1990, p. 186). It is implemented in the Wolfram Language as ...

The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

The great snub dodecicosidodecahedral graph is the skeleton of the great snub dodecicosidodecahedron, illustrated above in a few embeddings. It will be implemented in a ...

A graph with graph edges of two possible "colors," usually identified as red and blue. For a bichromatic graph with R red graph edges and B blue graph edges, R+B>=2.

The cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated cube. It is implemented in the Wolfram Language as ...

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance to a schematic illustration of a house ...

The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...