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The cube-connected cycle graph of order n is the graph obtained by replacing each vertex in a n-dimensional hypercube by a cycle of length n. They were introduced by ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

The Jack polynomials are a family of multivariate orthogonal polynomials dependent on a positive parameter alpha. Orthogonality of the Jack polynomials is proved in Macdonald ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

A prism graph, denoted Y_n, D_n (Gallian 1987), or Pi_n (Hladnik et al. 2002), and sometimes also called a circular ladder graph and denoted CL_n (Gross and Yellen 1999, p. ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...

The Heawood graph is a cubic graph on 14 vertices and 21 edges which is the unique (3,6)-cage graph. It is also a Moore graph. It has graph diameter 3, graph radius 3, and ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...