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The n-path complement graph P^__n is the graph complement of the path graph P_n. The first few are illustrated above. Since P_4 is self-complementary, P^__4 is isomorphic to ...

The pathwidth of a graph G, also called the interval thickness, vertex separation number, and node searching number, is one less than the size of the largest set in a path ...

The Patterson graph is the graph whose vertices are the 22880 centers of the Sylow 3-groups of the Suzuki group and in which two vertices are adjacent whenever they generate ...

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 ...

Erdős and Rényi (1960) showed that for many monotone-increasing properties of random graphs, graphs of a size slightly less than a certain threshold are very unlikely to have ...

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 planar embedding, also called a "plane graph" (Harary 1994, p. 103; Harborth and Möller 1994), "planar drawing," or "plane drawing," of a planar graph is an embedding in ...

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication (Wolfram 2002, pp. 5 and 716-717). More specifically, the ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

A pseudotree is a connected pseudoforest, i.e., an undirected connected graph that contains at most one graph cycle. Connected acyclic graphs (i.e., trees), are therefore ...