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Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

The complexity c_n of an integer n is the least number of 1s needed to represent it using only additions, multiplications, and parentheses. For example, the numbers 1 through ...

An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

There are two distinct entities both known as the Lagrange number. The more common one arises in rational approximation theory (Conway and Guy 1996), while the other refers ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

The (upper) matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree ...

There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...