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The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...

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 ...

A generalized octagon GO(n,k) is a generalized polygon of order 8. GO(1,2) is the (3,8)-cage graph, the incidence graph of the Cremona-Richmond configuration, the cubic ...

The small dodecahemidodecahedron is the uniform polyhedron with Maeder index 51 (Maeder 1997), Wenninger index 91 (Wenninger 1989), Coxeter index 65 (Coxeter et al. 1954), ...

Consider a finite collection of points p=(p_1,...,p_n), p_i in R^d Euclidean space (known as a configuration) and a graph G whose graph vertices correspond to pairs of points ...

The Kirchhoff sum index KfS is a graph index defined for a graph on n nodes by KfS=1/2sum_(i=1)^nsum_(j=1)^n((Omega)_(ij))/((d)_(ij)), where (Omega)_(ij) is the resistance ...

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

The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...