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A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

A Brunnian link is a set of n linked loops such that each proper sublink is trivial, so that the removal of any component leaves a set of trivial unlinked unknots. The ...

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

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).

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 ...

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 ...