Search Results for ""

A nilpotent Lie group is a Lie group G which is connected and whose Lie algebra is a nilpotent Lie algebra g. That is, its Lie algebra lower central series ...

Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

An outerplanar graph is a graph that can be embedded in the plane such that all vertices lie on the outer face. Outerplanar graphs are planar and, by their definition, ...

The pair group of a group G is the group that acts on the 2-subsets of {1,...,p} whose permutations are induced by G. Pair groups can be calculated using PairGroup[g] in the ...

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

The n-path complement graph P^__n is the graph complement of the path graph P_n. The first few are illustrated above. Since P_4 is self-complementary, P^__4 is isomorphic to ...

The Patterson graph is the graph whose vertices are the 22880 centers of the Sylow 3-groups of the Suzuki group and in which two vertices are adjacent whenever they generate ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n=1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, ...