图的双罗马控制数的上界

郝国亮; 庄蔚; 谢智红; 曾淑婷

doi:10.3969/j.issn.1000-1565.2023.05.001

河北大学学报(自然科学版) >

2023 , Vol. 43 >Issue 5: 449 - 452

DOI: https://doi.org/10.3969/j.issn.1000-1565.2023.05.001

图的双罗马控制数的上界

郝国亮 ,
庄蔚 ,
谢智红 ,
曾淑婷

展开

郝国亮(1980—),男,山东肥城人,菏泽学院副教授,博士,主要从事组合图论的研究.
E-mail:guoliang-hao@163.com

收稿日期: 2021-05-19

网络出版日期: 2023-10-25

基金资助

国家自然科学基金资助项目(12061007;11861011);江西省研究生创新专项资金资助项目(YC2021-S628)

收起

Upper bounds on the double Roman domination number in graphs

HAO Guoliang ,
ZHUANG Wei ,
XIE Zhihong ,
ZENG Shuting

Expand

1. School of Mathematics and Statistics, Heze University, Heze 274015, China; 2.College of Science, East China University of Technology, Nanchang 330013, China; 3. School of Mathematics and Statistics, Xiamen University of Technology, Xiamen 361024, China; 4. School of Business, Heze University, Heze 274015, China

Received date: 2021-05-19

Online published: 2023-10-25

Fold

摘要

通过对图的结构分析,利用图参数,如顶点数、直径、最小度以及填装数等,得到了连通图的双罗马控制数的若干新的上界.

关键词： 双罗马控制函数; 双罗马控制数; 直径; 填装数

本文引用格式

郝国亮 , 庄蔚 , 谢智红 , 曾淑婷 . 图的双罗马控制数的上界[J]. 河北大学学报(自然科学版), 2023 , 43(5) : 449 -452 . DOI: 10.3969/j.issn.1000-1565.2023.05.001

Abstract

By analyzing the structure of a graph and using the graph parameters, such as the number of vertices, diameter, minimum degree and packing number, some new upper bounds of the double Roman domination number of a connected graph are obtained.

Key words： double Roman dominating function; double Roman domination number; diameter; packing number

参考文献

[1] HAYNES T W, HEDETNIEMI S T, SLATER P J. Fundamentals of domination in graphs[M]. New York: Marcel Dekker, 1998.
[2] AHANGAR H A, AMJADI J, SHEIKHOLESLAMI S M,et al. Signed Roman edge domination numbers in graphs[J]. J Comb Optim, 2016, 31: 333-346.
[3] BENSON K F, FERRERO D, FLAGG M, et al. Nordhaus-Gaddum problems for power domination[J]. Discrete Appl Math, 2018, 251: 103-113.DOI: 10.1016/j.dam.2018.06.004.
[4] FAN W J, YE A S, MIAO F, et al. Outer-independent Italian domination in graphs[J]. IEEE Access, 2019, 7: 22756-22762.DOI: 10.1109/ACCESS.2019.2899875.
[5] HENNING M A, PAL S, PRADHAN D. Algorithm and hardness results on hop domination in graphs[J]. Inform Process Lett, 2020, 153:105872.DOI: 10.1016/j.ipl.2019.105872.
[6] 郝国亮,钱建国.有向图出控制数与入控制数的和[J].厦门大学学报(自然科学版),2015, 54(3): 351-353.DOI: 10.6043/j.issn.0438-0479.2015.03.010.
[7] OULDRABAH L, BLIDIA M, BOUCHOU A. Extremal digraphs for an upper bound on the Roman domination number[J]. J Comb Optim, 2019, 38: 667-679.DOI: 10.1007/s10878-019-00401-5.
[8] 赵衍才,单而芳.关于图的符号混合控制[J].应用数学学报,2020, 43(6): 915-922. DOI: 10.12387/C2020067.
[9] CHEN X. A note on the double Roman domination number of graphs[J]. Czechoslovak Math J, 2020, 70: 205-212. DOI: 10.21136/CMJ.2019.0212-18.
[10] HENNING M A, JAFARI RAD N. A characterization of double Roman trees [J]. Discrete Appl Math, 2019, 259: 100-111. DOI: 10.1016/j.dam.2018.12.033.
[11] JAFARI RAD N, RAHBANI H. Some progress on the double Roman domination in graphs [J]. Discuss Math Graph Theory, 2019, 39: 41-53. DOI: 10.7151/dmgt.2069.
[12] BONDY J A, MURTY U S R. Graph theory with applications [M]. London: Macmillan Press Ltd, 1976.
[13] BEELER R A, HAYNES T W, HEDETNIEMI S T. Double Roman domination[J]. Discrete Appl Math, 2016, 211: 23-29. DOI: 10.1016/j.dam.2016.03.017. (

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献