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Cubical Graph

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph , bipartite Kneser graph , 4-crossed prism graph, crown graph , grid graph , hypercube graph , and prism graph . It is illustrated above in a number of embeddings (e.g., Knuth 2008, p. 14).It has 12 distinct (directed) Hamiltonian cycles, corresponding to the unique order-4 LCF notation .It is a unit-distance graph, as shown above in a unit-distance drawing (Harborth and Möller 1994).The minimal planar integral drawings of the cubical graph, illustrated above, has maximum edge length of 2 (Harborth et al. 1987). They are also graceful (Gardner 1983, pp. 158 and 163-164). can be constructed as the graph expansion of with steps 1 and 1, where is a path graph. Excising an edge of the cubical graph gives the prism graph .The cubical graph has 8 nodes, 12 edges, vertex connectivity 3, edge connectivity..

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