【摘要】 一个有向图D称为本原有向图，若存在某自然数κ，使D中任一点u到任一点υ都有长为κ之途径．若D是一个对称有向图，则D是本原的当且仅当D对应的无向图G连通且至少包含一个奇圈．本文中，我们将决定具有最小奇圈长r的n阶对称本原有向图的第κ重上广义本原指数的最大数．更多还原

【Abstract】 A digraph D of order n is called primitive if there exists a positive integer k such that for each ordered pair of venices u and υ, there is a walk of length k from u to υ.If D is a symmetric digraph, then D is primitive if and only if its corresponding graph G is connected and contains at least one odd cycle. In this paper we determine the largest value of the kth upper generalized exponents over the set of primitive symmetric digraphs whose shortest odd cycle length is a fixed number r.更多还原