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The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A hypergraph is a graph in which generalized edges (called hyperedges) may connect more than two nodes.

An odd chordless cycle is a chordless cycle of length >4. A graph is said to be perfect iff neither the graph G nor its graph complement G^_ has an odd chordless cycle. A ...

An edge of a graph is said to be pendant if one of its vertices is a pendant vertex.

A vertex of a graph is said to be pendant if its neighborhood contains exactly one vertex.

A planar graph corresponding to polyhedra skeletons. The polyhedral graphs are special cases.

The nth-order Sierpiński carpet graph is the connectivity graph of black squares in the nth iteration of the Sierpiński carpet fractal. The first three iterations are shown ...

A graphical partitioning based on the eigenvalues and eigenvectors of the Laplacian matrix of a graph.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).