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A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

The Coxeter configuration is a 12_3 configuration whose Levi graph is the Nauru graph.

A graph is a forbidden (vertex-)induced subgraph if its presence as a vertex-induced subgraph of a given graph means it is not a member of some family of graphs. For example, ...

Two graphs are homeomorphic if there is a graph isomorphism from some graph subdivision of one to some subdivision of the other.

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

A unit-distance embedding is a graph embedding in which all edges have unit length. A graph possessing a unit-distance embedding in two dimensions is called a unit-distance ...

The Cox configuration is a (2^(d-1))_d configuration whose Levi graph is the d-hypercube graph.

Let G(V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t(n,k)<=((k-1)n^2)/(2k), where t(n,k) is the edge count. (Note ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

There are two versions of the moat-crossing problem, one geometric and one algebraic. The geometric moat problems asks for the widest moat Rapunzel can cross to escape if she ...