【摘要】 一个有向图称为本原的,如果存在正整数k,使得对每个顶点u到每个顶点v(可以是u)都有一条长为k的途径。如果G是本原的,这种最小的k称为G的本原指数,记作exp(G)。如果从某点u到某点v(可以是u)存在长为k和k+1的途径,这种最小的k称为G的Lewin数,记作l(G)。Jian Shen和Stewart Neufeld猜想,exp(G)≥2l(G)。本文就一类特殊的本原有向图证明猜想成立。更多还原

【Abstract】 A digraph G is primitive if for some positive integer k there is a walk of length exactly k from each vertex u to each vertex v (possiblely u again) . If G is primitive, the smallest such k is called the exponent of G, denoted by exp ( G). In 1971, M.Lewin introduced the parameter l ( G) for a primitive digraph G. It is the smallest k for which there is a both a walk of length k and a walk of length k + 1 from some vertex u to some vertex v (possiblely u again). Jian Shen and Steward Neufeld conjecture that exp(G)≥2l(G). In this paper, we will show that it’s true for a kind of special primitive digraph.更多还原