三条路笛卡尔积的全罗马控制Total Roman Domination on the Cartesian Product of Three Directed Paths
宋昕,张新鸿
摘要(Abstract)：
如果有向图D中每个赋值为0的顶点至少有一个赋值为2的内邻且D的由集合{v∈V(D):f(v)≠0}诱导出来的子图无孤立顶点，则称函数f:V(D)→{0,1,2}为D的一个全罗马控制函数。有向图D的全罗马控制函数的权为所有顶点的赋值之和，全罗马控制函数的最小权称为全罗马控制数。该文完全刻画了有向路笛卡尔积P_2×P_2×P_n的全罗马控制数。
关键词(KeyWords)： 笛卡尔积;全罗马控制函数;全罗马控制数;有向路
基金项目(Foundation): 山西省基础研究计划(20210302123202)
作者(Author): 宋昕,张新鸿
参考文献(References)：
- [1] LIU C H,CHANG G J.Roman domination on strongly chordal[J].Combin Optim,2013,26:608-619.
- [2] HAO G,ZHUANG W,HU K.Total Roman domination in digraphs[J].Quaest.Math,2019,40:1-18.
- [3] AHANGAR H A,HENNING M A,SAMODIVKIN V,et al.Total Roman domination in graphs[J].Appl.Anal.Discrete Math,2016,10:501-517.
- [4] AMJADI J,NAZARI-MOGHADDAM S,SHEIKHOLESLAMI S M,et al.Total Roman domination number of trees[J].Australas.J.Combin,2017,69:271-285.
- [5] AMJADI J,SHEIKHOLESLAMI S M,SOROUDI M.Nordhaus-Gaddum bounds for total Roman domination[J].Combin.Optim,2018,35:126-133.
- [6] HAO G.Total domination in digraphs[J].Quaest.Math,2017,40:333-346.
- [7] HENNING M A.Recent results on total domination in graphs:A survey[J].Discrete Math,2009,309:32-63.
- [8] BANG-JENSEN J,GUTIN G.Digraphs-theory,algorithms and applications[M].New York,Springer Publishing Company,Incorporated,2010.
- [9] SHEIKHOLESLAMI S M,VOLKMANN L.The Roman domination number of a digraph[J].Kragujevac Journal of Mathematics,2011,37:257-268.