Abstract
The thesis studies combinatorial properties of some graphs, known as Kac diagrams, which have important applications in algebra. We introduce an algorithm which converts a diagram to another. Two Kac diagrams are said to be equivalent if we can transform a diagram to another by a sequence of such algorithm. The main problem of this thesis is to study two simple Kac diagrams in the same G-orbit, determine whether they are equivalent. In the end, we have two conjectures based on above work.