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A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

For a connected bipartite graph G, the halved graph G^+ and G^- are the two connected components of the distance 2-graph of G. The following table summarizes some named ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

A noncayley graph is a graph which is not a Cayley graph. All graphs that are not vertex-transitive are noncayley graphs. However, some vertex-transitive graph are noncayley. ...

The pentagonal hexecontahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal hexecontahedron. It is implemented in the Wolfram Language as ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

The snub dodecahedron is an Archimedean solid consisting of 92 faces (80 triangular, 12 pentagonal), 150 edges, and 60 vertices. It is sometimes called the dodecahedron simum ...

The triakis icosahedral graph is Archimedean dual graph which is the skeleton of the triakis icosahedron. It is implemented in the Wolfram Language as ...

7 7 6 6 3 1; 6 5 4 2 ; 3 3 ; 2 A descending plane partition of order n is a two-dimensional array (possibly empty) of positive integers less than or equal to n such that the ...