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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 ...

The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

A unit-distance embedding is a graph embedding in which all edges have unit length. A graph possessing a unit-distance embedding in two dimensions is called a unit-distance ...