Search Results for ""

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

A complete k-partite graph is a k-partite graph (i.e., a set of graph vertices decomposed into k disjoint sets such that no two graph vertices within the same set are ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

Let A and B be any sets with empty intersection, and let |X| denote the cardinal number of a set X. Then |A|+|B|=|A union B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; ...

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ji):M_j->M_i i<=j be an R-module homomorphism. Call (M_i,sigma_(ji)) an inverse system over I ...

A set-like object in which order is ignored, but multiplicity is explicitly significant. Therefore, multisets {1,2,3} and {2,1,3} are equivalent, but {1,1,2,3} and {1,2,3} ...

A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

The vertex count of a graph g, commonly denoted V(g) or |g|, is the number of vertices in g. In other words, it is the cardinality of the vertex set. The vertex count of a ...