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The Poussin graph is the 15-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 rising sun graph is the graph on 7 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["RisingSunGraph"].

The Schläfli double sixes graph is the Levi graph of the double sixes configuration.

The cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron. It is implemented in the Wolfram Language as ...

The pentagonal wedge graph is the skeleton of the pentagonal wedge. It is a has 8 vertices, 12 edges, and 6 faces. The pentagonal wedge graph is implemented in the Wolfram ...

The truncated dodecadodecahedral graph is the skeleton of the truncated dodecadodecahedron, which is the only uniform polyhedron for which this is the case. It will be ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

An empty graph on n nodes consists of n isolated nodes with no edges. Such graphs are sometimes also called edgeless graphs or null graphs (though the term "null graph" is ...

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...

The banner graph is the (4,1)-tadpole graph illustrated above. It could perhaps also be termed the 'P graph.' It is implemented in the Wolfram Language as ...