三条路笛卡尔积的全罗马控制  

Total Roman Domination on the Cartesian Product of Three Directed Paths

作　　者：宋昕 张新鸿[1] SONG Xin;ZHANG Xin-hong(School of Applied Sciences,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院,太原030024

出　　处：《太原科技大学学报》2025年第1期77-81,共5页Journal of Taiyuan University of Science and Technology

基　　金：山西省基础研究计划(20210302123202)。

摘　　要：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P2×P2×P_n的全罗马控制数。A function f:V(D)→{0,1,2}defined on the vertex set V(D)of a digraph D is called a total Roman dominating function on D if any vertex assigned 0 is adjacent to at least one in-neighbour assigned 2 and the subdigraph of D induced by the set{v∈V(D):f(v)≠0}has no isolated vertex.The weight of a total Roman dominating function is the sum of assigned values of all vertices.The total Roman domination number of a digraph D is defined as the minimum weight of a total Roman dominating function on D.In this paper,we determined the total Roman domination number of P 2×P 2×P n.

关 键 词：笛卡尔积 全罗马控制函数 全罗马控制数 有向路 

分 类 号：O157.5[理学—数学]