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The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

Miller's rules, originally devised to restrict the number of icosahedron stellations to avoid, for example, the occurrence of models that appear identical but have different ...

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 ...

The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

A nonhamiltonian graph is a graph that is not Hamiltonian. All disconnected graphs are therefore nonhamiltoinian, as are acylic graphs. Classes of connected graphs that are ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

An open connected set is called a region (sometimes also called a domain).

The cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated cube. It is implemented in the Wolfram Language as ...