Abstract:

Let H be a hypergraph. The author uses the notations H\+* and L(H) to mean the dual hypergraph and line graph of H respectively. The adjacent graph of H, denoted by G\-H, is defined to be the graph which consist of L(H\+*) and the loops of H. If G\-H is primitive, then H is called primitive, and γ(G\-H) is called the exponent of H. In this paper, the author obtains that the exponent set of primitive simple hypergraphs of order n and the exponent set of primitive simple hypergraphs of order n with rank at least 3. Further, the extremal hypergraphs are described.

Key words:  Hypergraph, Adjacent graph of hypergraph, Primitive hypergraph