On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs

被引：12
|
作者：
Hayat, Sakander [1 ]
Khan, Asad [2 ]
Zhong, Yubin [1 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China
[2] Guangzhou Univ, Sch Comp Sci & Cyber Engn, Guangzhou 510006, Peoples R China
来源：
MATHEMATICS | 2022年 / 10卷 / 11期
关键词：
graph; resolving set; dominating set; metric-dominating set; complete multipartite graph; MIXED METRIC DIMENSION; NUMBER; PRODUCT; CODES; SETS; P(N;
D O I：
10.3390/math10111815
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n, which provides an infinite family of counterexamples to the characterization. Furthermore, we find exact values of the metric, edge metric, mixed-metric dimensions, the domination number, locating-dominating number, and metric-locating-dominating number for the complete multipartite graphs. These results generalize various results in the literature from complete bipartite to complete multipartite graphs.
引用
收藏
页数：16
相关论文
共 50 条
  • [1] Domination-related parameters in middle graphs
    Kim, Kijung
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2024, 16 (05)
  • [2] Domination-Related Parameters in Rooted Product Graphs
    Dorota Kuziak
    Magdalena Lemańska
    Ismael G. Yero
    Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39 : 199 - 217
  • [3] Domination-Related Parameters in Rooted Product Graphs
    Kuziak, Dorota
    Lemanska, Magdalena
    Yero, Ismael G.
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 (01) : 199 - 217
  • [4] Signed and Minus Domination in Complete Multipartite Graphs
    Liang, Hongyu
    ARS COMBINATORIA, 2016, 126 : 133 - 142
  • [5] New Bounds for Three Outer-Independent Domination-Related Parameters in Cactus Graphs
    Cabrera-Martinez, Abel
    Rueda-Vazquez, Juan Manuel
    Segarra, Jaime
    AXIOMS, 2024, 13 (03)
  • [6] The p-domination number of complete multipartite graphs
    Lu, You
    Xu, Jun-Ming
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2014, 6 (04)
  • [7] Maximal matching and edge domination in complete multipartite graphs
    Song, Wenyao
    Miao, Lianying
    Wang, Haichao
    Zhao, Yancai
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2014, 91 (05) : 857 - 862
  • [8] Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs
    Yancai ZHAO
    Journal of Mathematical Research with Applications, 2023, 43 (02) : 161 - 165
  • [9] On graphs with complete multipartite μ-graphs
    Jurisic, Aleksandar
    Munemasa, Akihiro
    Tagami, Yuki
    DISCRETE MATHEMATICS, 2010, 310 (12) : 1812 - 1819
  • [10] On Resolvability Parameters of Some Wheel-Related Graphs
    Yang, Bin
    Rafiullah, Muhammad
    Siddiqui, Hafiz Muhammad Afzal
    Ahmad, Sarfraz
    JOURNAL OF CHEMISTRY, 2019, 2019
12345