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A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

"The" tetrahedral graph is the Platonic graph that is the unique polyhedral graph on four nodes which is also the complete graph K_4 and therefore also the wheel graph W_4. ...

The word net has several meanings in mathematics. It refers to a plane diagram in which the polyhedron edges of a polyhedron are shown, a point set satisfying certain ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

A cactus graph, sometimes also called a cactus tree, a mixed Husimi tree, or a polygonal cactus with bridges, is a connected graph in which any two graph cycles have no edge ...