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In general, a triakis tetrahedron is a non-regular dodecahedron that can be constructed as a positive augmentation of a regular tetrahedron. Such a solid is also known as a ...

A polyomino is a generalization of the domino to a collection of n squares of equal size arranged with coincident sides. Polyominos were originally called "super-dominoes" by ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...

Cantellation, also known as (polyhedron) expansion (Stott 1910, not to be confused with general geometric expansion) is the process of radially displacing the edges or faces ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...