有向图字典式积中D(n,p)结构的存在性  

Existence of D(n,p) in Lexicographic Product of Digraphs

作　　者：巩雨 刘娟[1] GONG Yu;LIU Juan(College of Mathematical Sciences,Xinjiang Normal University,Urumqi 830017,China)

机构地区：[1]新疆师范大学数学科学学院

出　　处：《西华师范大学学报（自然科学版）》2019年第4期371-375,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11761071);新疆师范大学“十三五”校级重点学科数学招标课题资助项目(17SDKD1107);新疆维吾尔自治区“天山青年计划”优秀青年科技人才培养项目(2017Q025)

摘　　要：关于有向图的一个非常重要的研究方向是有向图中的圈,D(n,p)结构作为有向图中一类特殊的圈结构,近年来被越来越多的学者研究。对于两个整数2≤p≤n和n≥3,用D(n,p)表示在n个点的有向图中由长度为n的有向圈通过改变连续p-1条弧的方向。本文证明了包含哈密尔顿圈及D(m,p m)结构的m阶有向图和另一个q阶有向图的字典式积有向图包含D(qm,p)结构,2≤p≤qm,并在此基础上给出了正则一致m-部(m≥5)竞赛图中D(qm,p)结构的存在性这一推论。Cycle is an important research field of digraphs.In recent years,the structure of D(n,p)as a specified cycle of digraphs has been studied by more and more scholars.For two integers 2≤p≤n and n≥3,D(n,p)denotes the digraph with n vertices obtained from a directed cycles of length by n changing the orientation of p-1 consecutives arcs.In this paper,the existence of the D(qm,p)in lexicographic product of two digraphs is proved,including Hamiltionian digraph containing D(m,p m)of order m and a digraph of order q,2≤p≤qm.Moreover,it is deduced that regular ordinary m-partite(m≥5)tournaments contain D(qm,p).

关 键 词：有向图 圈 字典式积 一致多部竞赛图 D(n p)结构 

分 类 号：O157.5[理学—数学] O157.6[理学—基础数学]