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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 ...

A "square" word consists of two identical adjacent subwords (for example, acbacb). A squarefree word contains no square words as subwords (for example, abcacbabcb). The only ...

The star graph S_n of order n, sometimes simply known as an "n-star" (Harary 1994, pp. 17-18; Pemmaraju and Skiena 2003, p. 248; Tutte 2005, p. 23), is a tree on n nodes with ...

The Steinmetz solid is the solid common to two (or three) right circular cylinders of equal radii intersecting at right angles is called the Steinmetz solid. Two cylinders ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

"The" Sylvester graph is a quintic graph on 36 nodes and 90 edges that is the unique distance-regular graph with intersection array {5,4,2;1,1,4} (Brouwer et al. 1989, ...

A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

Let L(n,d) be the smallest tour length for n points in a d-D hypercube. Then there exists a smallest constant alpha(d) such that for all optimal tours in the hypercube, lim ...

The triangular graph T_n=L(K_n) is the line graph of the complete graph K_n (Brualdi and Ryser 1991, p. 152). The vertices of T_n may be identified with the 2-subsets of ...