Mohammad Hamidi - Dept. of Math., Faculty of Mathematics, Payame Noor University, Tehran, Iran
Arsham Borumand Saeid - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, ‎Kerman, Iran‎

This paper defines the concept of partitioned hypergraphs‎, ‎and enumerates the number of these hypergraphs and discrete complete hypergraphs‎. ‎A positive equivalence relation is defined on hypergraphs‎, ‎this relation establishes a connection between hypergraphs and graphs‎. ‎Moreover‎, ‎we define 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.

(Hyper)graph, derivable graphs, positive equivalence relation