On biconnected graphs - Gonzaga, Alex C. (Animo Repository, 1995)
A graph G is said to be biconnected if G and its complement G prime are connected.This study, presents and proves necessary and sufficient conditions for biconnectedness of graphs, in general, and trees, in particular. It also introduces and investigates properties of a new class of graphs known as the maximal biconnected graphs. Furthermore, the study states and proves a theorem on the greatest lower bound and least upper bound of independence, dominance, chromatic and connectivity numbers of biconnected graphs of order n equal to or greater than 4. A simple formula that also specifies characteristic number - nullity - is applied in proving theorems concerning biconnected graphs G such that both G and G prime satisfy specified properties. Also, it states and proves properties of some graph operations on biconnected graphs such as graphing, sum, cartesian product and conjunction. Finally, a theorem on the diameter of biconnected graph is stated and proved.