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The pentakis icosidodecahedral graph, illustrated above, is a graph on 42 vertices that is the skeleton of the pentakis icosidodecahedron.

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is ...

The skeleton of a trapezohedron may be termed a trapezohedral graph. n-trapezohedral graphs are illustrated above for n=3 to 10 in circular embeddings with the two interior ...

"The" square graphs is the cycle graph C_4. It is isomorphic to the complete bipartite graph K_(2,2). Like all cycle graphs, the line graph of C_4 is isomorphic to itself. A ...

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

A cubic semisymmetric graph is a graph that is both cubic (i.e., regular of degree 3) and semisymmetric (i.e., edge- but not vertex-transitive). The four smallest cubic ...

The domino graph is the graph on 6 vertices illustrated above. It is isomorphic to the 3-ladder graph and the (2,3)-grid graph. It is implemented in the Wolfram Language as ...

The fork graph, sometimes also called the chair graph, is the 5-vertex tree illustrated above. It could perhaps also be known as the 'h graph' (but not to be confused with ...

The Kummer graph is the name apparently first adopted here for the Levi graph of Kummer's 16_6 configuration (Coxeter 1950), corresponding to the folded 6-cube graph (Brouwer ...

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"].