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In a graph G, two graph vertices are adjacent if they are joined by a graph edge.

The use of techniques from algebra, topology, and geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas ...

The determination of the number of alternating permutations having elements {1,2,...,n}.

1. A fixed polyomino. 2. The set of points obtained by taking the centers of a fixed polyomino.

An antimagic graph is a graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex differ.

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 ...