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The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

Every finite group of order n can be represented as a permutation group on n letters, as first proved by Cayley in 1878 (Rotman 1995).

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

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 ...

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

The clique graph of a given graph G is the graph intersection of the family of cliques of G. A graph G is a clique graph iff it contains a family F of complete subgraphs ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

An n-component of a graph G is a maximal n-connected subgraph.