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The Errera graph is the 17-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

The icosahedral graph is the Platonic graph whose nodes have the connectivity of the regular icosahedron, as well as the great dodecahedron, great icosahedron Jessen's ...

The small rhombicosidodecahedral graph is a quartic graph on 60 nodes and 120 edges that corresponds to the skeleton of the small rhombicosidodecahedron, as well as the great ...

The deltoidal hexecontahedral graph is an Archimedean dual graph which is the skeleton of the deltoidal hexecontahedron as well as the rhombic hexecontahedron. It is ...

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

The truncated tetrahedral graph is the cubic Archimedean graph on 12 nodes and 18 edges that is the skeleton of the truncated tetrahedron. It is implemented in the Wolfram ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

The Harries graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries-Wong graph. The Harries graph is ...

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 Heawood four-color graph is the 25-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's ...