Document Type: Research Paper
Dept. of Math., Faculty of Mathematics, Payame Noor University, Tehran, Iran
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.