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Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

The Barnette-Bosák-Lederberg graph is a graph on 38 vertices which is the smallest known example of a planar 3-connected nonhamiltonian graph, i.e., the smallest known ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

The bipartite double graph, also called the Kronecker cover, Kronecker double cover, bipartite double cover, canonical double cover, or bipartite double, of a given graph G ...

A biquadratic number is a fourth power, n^4. The first few biquadratic numbers are 1, 16, 81, 256, 625, ... (OEIS A000583). The minimum number of biquadratic numbers needed ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

A complete bipartite graph, sometimes also called a complete bicolored graph (Erdős et al. 1965) or complete bigraph, is a bipartite graph (i.e., a set of graph vertices ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...