一类本原无向图的重上广义本原指数集

The Set of k th Upper Generalized Exponents for a Class of Primitive Graphs

设Ｒ（ｎ，ｄ）表示由全体恰含ｄ个环点的ｎ（ｎ≥３）阶本原无向图所构成的集合，Ｆ（ｎ，ｄ，ｋ）为Ｒ（ｎ，ｄ）中图的第ｋ重上广义本原指数的最大值，１≤ｄ≤ｎ，２≤ｋ≤ｎ－１．本文给出了Ｆ（ｎ，ｄ，ｋ）的具体形式，并证明了Ｒ（ｎ，ｄ）的第ｋ重上广义本原指数集为Ｅ（ｎ，ｄ，ｋ）＝｛１，２，…，Ｆ（ｎ，ｄ，ｋ）｝．

Let R(n,d) be a set of primitive symmetric digraphs of order n with exact d vertices having ring. F(n,d,k) be the largest value of the k th upper generalized exponents of the R(n,d) . In this paper we give the expression of F(n,d,k) , and prove the set of k th upper generalized exponents of the R(n,d) is E(n,d,k)={1,2,… ,F(n,d,k) } .