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Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

A directed graph is called an arborescence if, from a given node x known as the root vertex, there is exactly one elementary path from x to every other node y.

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The 4-polyhex illustrated above (Gardner 1978, p. 147).

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

A Sheffer sequence for (1,f(t)) is called the associated sequence for f(t), and a sequence s_n(x) of polynomials satisfying the orthogonality conditions ...

The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its ...

A pattern tau=(tau_1,...,tau_n) is said to avoid alpha=(alpha_1,...,alpha_k) if alpha is not contained in tau. In other words, tau avoids alpha iff no k-subset of tau is ...

The property of certain algorithms that accurate answers are returned for well-conditioned problems, and the inaccuracy of the answers returned for ill-conditioned problems ...

A polyhex consisting of hexagons arranged along a line.