一类有环的双色有向图的本原指数  

Exponents of a Class of Two-colored Digraphs with Loops

作　　者：林建青[1] 

机构地区：[1]山西大同大学朔州师范分校数计系,山西朔州036002

出　　处：《绵阳师范学院学报》2012年第5期10-12,24,共4页Journal of Mianyang Teachers＇ College

摘　　要：一个双色有向图的D是本原的,当且仅当存在非负整数h和k,且h+k>0,使得D中的每一对顶点(i,j)都存在从i到j的(h,k)途径,此时称h+k的最小值为D的本原指数.利用代数与图论的方法,研究一类带有环的双色有向圈的本原指数,给出了本原指数和本原指数上界。A two - colored digraph D is primitive if, and only if there exist nonnegative integers h and k with h ＋ k 〉 0 such that for each pair （ i ; j） of vertices, there exists an （ h ; k） - walk in D from i to j. The expo- nent of the primitive two - colored digraph D is the minimum value of h ＋ k taken over all such h and k. In this paper,the exponents of a class of two - colored digraphs with loops is taken into consideration, and hence, the primitive conditions and the upper bounds on the exponents are obtained.

关 键 词：双色有向图 环 本原指数 

分 类 号：O157[理学—数学]