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A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

A heptahedral graph is a polyhedral graph on seven nodes. There are 34 nonisomorphic heptahedral graphs, as first enumerated by Kirkman (1862-1863) and Hermes (1899ab, 1900, ...

The large Witt graph, also called the octad graph (Brouwer) or Witt graph (DistanceRegular.org), is the graph whose vertices are the 759 blocks of a Steiner system S(5,8,24) ...

A theorem stated in 1882 which cannot be derived from Euclid's postulates. Given points a, b, c, and d on a line, if it is known that the points are ordered as (a,b,c) and ...

The point-slope form of a line through the point (x_1,y_1) with slope m in the Cartesian plane is given by y-y_1=m(x-x_1).

The double graph of a given graph G is constructed by making two copies of G (including the initial edge set of each) and adding edges u_1v_2 and v_1u_2 for every edge uv of ...

The complement of a graph G, sometimes called the edge-complement (Gross and Yellen 2006, p. 86), is the graph G^', sometimes denoted G^_ or G^c (e.g., Clark and Entringer ...

Let V(G) be the vertex set of a simple graph and E(G) its edge set. Then a graph isomorphism from a simple graph G to a simple graph H is a bijection f:V(G)->V(H) such that ...

The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

A graph H is called a topological minor, also known as a homeomorphic subgraph, of a graph G if a graph subdivision of H is isomorphic to a subgraph of G. Every topological ...