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A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...

The truncated pentakis dodecahedral graph, illustrated above in a pair of embeddings, is the skeleton of the truncated pentakis dodecahedron. It has 180 vertices, 270 edges, ...

The Shi-Krotov-Solé graph is a weakly regular graph on 1024 vertices with regular parameters (nu,k,lambda,mu)=(1024,33,2,(0,2)). It is distance-regular but not ...

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 ...