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The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

An antiprism graph is a graph corresponding to the skeleton of an antiprism. Antiprism graphs are therefore polyhedral and planar. The n-antiprism graph has 2n vertices and ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...

A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

A synonym for integer. The word "rational" is sometimes used for emphasis to distinguish it from other types of "integers" such as cyclotomic integers, Eisenstein integers, ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

The Icosian game, also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a ...