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The Perkel graph is a weakly regular graph on 57 vertices and 171 edges, shown above in several embeddings. It is the unique distance-regular graph with intersection array ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...

The tetrakis hexahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

A universal cellular automaton is a cellular automaton which, like a Turing machine, exhibits universality. von Neumann proved that an automaton consisting of cells with four ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A cubic polyhedral graph is a graph that is both cubic and polyhedral. The numbers of cubical polyhedral graphs on n=2, 4, ... nodes are 0, 1, 1, 2, 5, 14, 50, 233, 1249, ... ...