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

The paw graph is the 3-pan graph, which is also isomorphic to the (3,1)-tadpole graph. It is implemented in the Wolfram Language as GraphData["PawGraph"].

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

The dart graph is the 5-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["DartGraph"].

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 ...

Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform ...

The Doob graph D(m,n) is the graph given by the graph Cartesian product of m>=1 copies of the Shrikhande graph with a Hamming graph H(n,4). Doob graphs are distance-regular ...

The moth graph is the 6-vertex graph illustrated above. It is implemented in the Wolfram Language as GraphData["MothGraph"].

The A graph is the graph on 6 vertices illustrated above. Unfortunately, at least one author (Farrugia 1999, p. 2) uses the term "A-graph" to refer to the 5-node bull graph. ...