ON DERIVABLE TREES

This paper denes the concept of partitioned hypergraphs, and enumerates the number of these hypergraphs and discrete complete hypergraphs. A positive equivalence relation is dened on hypergraphs, this relation establishes a connection between hypergraphs and graphs. Moreover, we dene the concept of (extended) derivable graph. Then a connection between hypergraphs and (extended) derivable graphs was investigated. Via the positive equivalence relation on hypergraphs, we show that some special trees are derivable graph and complete graphs are self derivable graphs.