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The shortest path problem seeks to find the shortest path (a.k.a. graph geodesic) connecting two specific vertices (u,v) of a directed or undirected graph. The length of the ...

A simple function is a finite sum sum_(i)a_ichi_(A_i), where the functions chi_(A_i) are characteristic functions on a set A. Another description of a simple function is a ...

The Soicher graphs are three distance-regular graphs on 5346, 486, and 315 vertices, respectively. The first two are also distance-transitive but the third is not. The second ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A graph is strongly perfect if every induced subgraph H has an independent vertex set meeting all maximal cliques of H (Berge and Duchet 1984, Ravindra 1999). Every strongly ...

The Suetake graph is a weakly regular Hamiltonian graph on 231 vertices with parameters (nu,k,lambda,mu)=(72,(12),(0),(0,4)). It is distance-regular with intersection array ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

In category theory, a tensor category (C, tensor ,I,a,r,l) consists of a category C, an object I of C, a functor tensor :C×C->C, and a natural isomorphism a = a_(UVW):(U ...

Color each segment of a knot diagram using one of three colors. If 1. At any crossing, either the colors are all different or all the same, and 2. At least two colors are ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...