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A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

The Foster cage is one of the four (5,5)-cage graphs. Like the other (5,5)-cages, the Foster cage has 30 nodes. It has 75 edges, diameter 3, girth 5, chromatic number 4, and ...

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

An induced subgraph is a subgraph obtained from an original graph by removing a subset of vertices and/or edges together with any edges whose endpoints are both in this ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

A 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

The Császár polyhedron is a polyhedron that is topologically equivalent to a torus which was discovered in the late 1940s by Ákos Császár (Gardner 1975). It has 7 polyhedron ...

The term multigraph refers to a graph in which multiple edges between nodes are either permitted (Harary 1994, p. 10; Gross and Yellen 1999, p. 4) or required (Skiena 1990, ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...