本原简单超图的指数集

The Exponent Set of Primitive Simple Hypergraphs

设H是一个超图,用H 和L(H)分别表示H的对偶超图和线图.定义H的邻接图是由L(H )和H的所有环组成的图,记作GH.若GH 是本原的,则称H是本原的,并称γ(GH)为H的指数.该文得到了所有n阶本原简单超图以及所有秩不小于 3的n阶本原简单超图的指数集。

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.