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A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

There exists an integer N such that every string in the look and say sequence "decays" in at most N days to a compound of "common" and "transuranic elements." The table below ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A cyclic quadrilateral is a quadrilateral for which a circle can be circumscribed so that it touches each polygon vertex. A quadrilateral that can be both inscribed and ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

The great rhombicuboctahedron (Cundy and Rowlett 1989, p. 106) is the 26-faced Archimedean solid consisting of faces 12{4}+8{6}+6{8}. It is sometimes called the ...

In a 1847 talk to the Académie des Sciences in Paris, Gabriel Lamé (1795-1870) claimed to have proven Fermat's last theorem. However, Joseph Liouville immediately pointed out ...

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 ...