设D是一个本原有向图,则存在正整数k,使得对D中某两点u,v,在D中从u到v有长为k和k+1的有向途径,这样的最小正整数k称为D的Lewin指数.本文给出围长为3的n阶本原有向图的Lewin指数集l(Dn,3):l(D4,3)={1};l(Dn,3)={1,2,…,n-2}(n≥5).
Let D be a primitive digraph, then there exists a non-negative integer k such that for some u,v ∈ V(D) there are two walks of lengths k and k+1 from u to v. The least k is called the Lewin index of the digraph D. In this paper, we consider the Lewin index of primitive digraphs with order n and girth 3, and obtain the following results :l(Dn,3):l(D4,3)={1};l(Dn,3)={1,2,…,n-2}(n≥5).