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Given a positive integer n, a labeled n-digraph is a digraph whose vertex set is {1,...,n}.

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

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 ...

If G is a weighted tree with weights w_i>1 assigned to each vertex v_i, then G is perfectly weighted if the matrix M_G=[w_1 0 ... 0; 0 w_2 ... 0; | ... ... |; 0 0 ... ...

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

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

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 ...

Heule graphs are a set of unit-distance graphs with chromatic number five derived by Marijn Heule in April 2018 to July 2918 from the 1581-vertex de Grey Graph (Heule 2018). ...