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Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.

The set of all centroid points in a weighted tree (Harary 1994, p. 36).

Let J be a finite group and the image R(J) be a representation which is a homomorphism of J into a permutation group S(X), where S(X) is the group of all permutations of a ...

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

A tensor which has the same components in all rotated coordinate systems. All rank-0 tensors (scalars) are isotropic, but no rank-1 tensors (vectors) are. The unique rank-2 ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping, every person ...

The 120-cell is a finite regular four-dimensional polytope with Schläfli symbol {5,3,3}. It is also known as the hyperdodecahedron or hecatonicosachoron, and is composed of ...

A point in a weighted tree that has minimum weight for the tree. The set of all centroid points is called a tree centroid (Harary 1994, p. 36). The largest possible values ...