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A half-plane is a planar region consisting of all points on one side of an infinite straight line, and no points on the other side. If the points on the line are included, ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

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 ...

Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki ...

The snub cubical graph is the Archimedean graph on 24 nodes and 60 edges obtained by taking the skeleton of the snub cube. It is a quintic graph, is planar, Hamiltonian, and ...

For a graph vertex x of a graph, let Gamma_x and Delta_x denote the subgraphs of Gamma-x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The ...

A one-dimensional geometric object such as a pencil or line segment range.

Three sets of three lines such that each line is incident with two from both other sets.

A function f(x) has a vertical tangent line at x_0 if f is continuous at x_0 and lim_(x->x_0)f^'(x)=+/-infty.

A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching. Conversely, a graph that can be reduced to ...