ABSTRACT
The connectivity of graphs is a particularly intuitive area of graph theory and extends the concepts of cutpoint, bridge, and block. There is a rich body of theorems concerning connectivity. Many of these are variations of a classical result of K. Menger, which involves the number of disjoint paths joining a given pair of points in a graph. The problem of determining the largest connectivity possible for a graph with a given number of points and lines was proposed by C. Berge and a solution was given. In 1927 Menger showed that the connectivity of a graph is related to the number of disjoint paths joining distinct points in the graph. Chronologically the variation of Menger's Theorem was published by Whitney in a paper in which he included a criterion for a graph to be n-connected.
