Search Results for ""

An edge-transitive graph is a graph such that any two edges are equivalent under some element of its automorphism group. More precisely, a graph is edge-transitive if for all ...

A geometry in which Euclid's fifth postulate holds, sometimes also called parabolic geometry. Two-dimensional Euclidean geometry is called plane geometry, and ...

The Franklin graph is the 12-vertex cubic graph shown above whose embedding on the Klein bottle divides it into regions having a minimal coloring using six colors, thus ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

An invertible knot is a knot that can be deformed via an ambient isotopy into itself but with the orientation reversed. A knot that is not invertible is said to be ...

The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle (cf. Garnder 1986, pp. 137-138). While the ...

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

The (m,n)-lollipop graph is the graph obtained by joining a complete graph K_m to a path graph P_n with a bridge. Precomputed properties of lollipop graphs are available in ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...