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The great snub dodecicosidodecahedral graph is the skeleton of the great snub dodecicosidodecahedron, illustrated above in a few embeddings. It will be implemented in a ...

A graph whose nodes are sequences of symbols from some alphabet and whose edges indicate the sequences which might overlap. The above figures show the first few n-dimensional ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...

A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...

The (26,8)-Paulus graph having the largest possible graph automorphism group order of all 26-node Paulus graphs (namely 120) is sometimes known as the ...

The doubly truncated Witt graph is the graph on 330 vertices related to a 3-(22,8,12) design (Brouwer et al. 1989, p. 367). The doubly truncated Witt graph can be constructed ...

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 ...

A planar hypohamiltonian graph is a hypohamiltonian graph that is also planar. A number of planar hypohamiltonian graphs are illustrated above. Chvátal (1973) first asked if ...

A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...