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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (11): 21-25.doi: 10.6040/j.issn.1671-9352.0.2021.003

• • 上一篇    

图的双罗马控制数的界

谢智红,郝国亮*   

  1. 东华理工大学理学院, 江西 南昌 330013
  • 发布日期:2022-11-10
  • 作者简介:谢智红(1978— ),女,博士,副教授,研究方向为企业管理、运筹与优化. E-mail:xiezh168@ecut.edu.cn*通信作者简介:郝国亮(1980— ),男,博士,副教授,硕士生导师,研究方向为组合图论. E-mail:guoliang-hao@163.com
  • 基金资助:
    国家自然科学基金资助项目(12061007,11861011)

Bounds on the double Roman domination number of graphs

XIE Zhi-hong, HAO Guo-liang*   

  1. College of Science, East China University of Technology, Nanchang 330013, Jiangxi, China
  • Published:2022-11-10

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摘要： 定义在图G的顶点集V(G)上的函数f:V(G)→{0,1,2,3}称为G的双罗马控制函数,如果每个赋值为0的顶点至少与一个赋值为3或两个赋值为2的顶点相邻,并且每个赋值为1的顶点至少与一个赋值为2或3的顶点相邻。图的双罗马控制函数的权为所有顶点的赋值之和。双罗马控制函数的最小权称为双罗马控制数。利用顶点数、围长、周长以及最小度得到了含圈图的双罗马控制数的若干上下界。

Abstract: A function f:V(G)→{0,1,2,3}defined on the vertex set V(G)of a graph G is called a double Roman dominating function if any vertex assigned 0 is adjacent to at least one vertex assigned 3 or two vertices assigned 2, and any vertex assigned 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a double Roman dominating function is the sum of assigned values of all vertices. The double Roman domination number of a graph G is defined as the minimum weight of a double Roman dominating function on G. Using the number of vertices, girth, circumference and minimum degree of graphs, some lower and upper bounds on the double Roman domination number of graphs with a cycle are established.

Key words: double Roman dominating function, double Roman domination number, girth, circumference

中图分类号: 

  • O157.5
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