一类含有两个(n-1)-圈的三色有向图本原指数

Primitive exponents of a class of three-colored digraphs with two(n-1)-cycles

为研究非负矩阵簇的本原指数问题,将双色有向图推广到三色有向图.利用有向图与矩阵的对应关系,研究了一类三色有向图,它的未着色图中包含n个顶点,一个n-圈和两个(n-1)-圈,给出了本原条件,指数上界,并对达到指数上界的极图进行了刻画.

In order to study the primitive exponent problem of nonnegative matrix pairs,the two-colored digraphs are extended to three-colored digraphs.Using the corresponding relation between a digraph and a matrix,a class of primitive three-colored digraphs whose uncolored digraphs has n vertices,consists of one n-cycle and two(n-1)-cycles is studied.Some primitive conditions,a tight upper bound of primitive exponents and the characterization of extremal three-colored digraphs are given.