[1]郝国亮.笛卡尔乘积有向图C2×Cn与C3×Cn的 3-彩虹控制数[J].延边大学学报(自然科学版),2016,42(01):11-14.
　HAO Guoliang.The 3-rainbow domination number of the Cartesian products digraph C2Cn and C3Cn[J].Journal of Yanbian University,2016,42(01):11-14.
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笛卡尔乘积有向图C2×Cn与C3×Cn的 3-彩虹控制数

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第42卷 期数: 2016年01期 页码: 11-14 栏目: 基础科学研究 出版日期: 2016-03-20
Title:
The 3-rainbow domination number of the Cartesian products digraph C2ࢧCn and C3ಏCn
作者:
郝国亮
东华理工大学理学院 数学系, 江西 南昌 330013
Author(s):
HAO Guoliang
Department of Mathematics, College of Science, East China University of Technology, Nanchang 330013, China
关键词:
彩虹控制函数;  彩虹控制数;  笛卡尔乘积
Keywords:
rainbow dominating function;  rainbow domination number;  Cartesian product
分类号:
O157.5
文献标志码:
A
摘要:
设γr k(D)是有向图D的k-彩虹控制数且设Cm×Cn是m长有向圈Cm与n长有向圈Cn的笛卡尔乘积有向图.用构造的方法找到了笛卡尔乘积有向图C2×Cn与C3×Cn的3-彩虹控制数的上界,并证明了此上界恰好为其下界,即得到了γr3(C2×Cn)与γr3(C3×Cn)的精确值.
Abstract:
Let γr k(D)be the k -rainbow domination number of a digraph D, and let Cm×Cn be the Cartesian product digraph of the directed cycle Cm of length m and the directed cycle Cn of length n. The upper bounds on 3-rainbow domination number of C2ࢧCn and C3ಏCn are found by construction methods, which are exactly the lower bounds, that is, the exact values of γr3(C2緗Cn)and γr3(C3膿Cn)are obtained.

参考文献/References:

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备注/Memo

收稿日期: 2016-01-26 作者简介: 郝国亮(1980—),男,博士,讲师,研究方向为组合图论. 基金项目: 江西省教育厅科学技术研究项目(GJJ150561); 东华理工大学博士科研启动基金资助项目(DHBK2015319,DHBK2015320)

更新日期/Last Update: 2016-01-20