The edge partition dimension of graphs

被引：0
|
作者：
Kuziak, Dorota [1 ]
Maritz, Elizabeth [2 ]
Vetrik, Tomas [2 ]
Yero, Ismael G. [3 ]
机构：
[1] Univ Cadiz, Dept Estat & Invest Operat, Algeciras, Spain
[2] Univ Free State, Dept Math & Appl Math, Bloemfontein, South Africa
[3] Univ Cadiz, Dept Matemat, Algeciras, Spain
来源：
DISCRETE MATHEMATICS LETTERS | 2023年 / 12卷
基金：
新加坡国家研究基金会;
关键词：
edge resolving partition; edge partition dimension; edge metric dimension; partition dimension;
D O I：
10.47443/dml.2023.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The edge metric dimension was introduced in 2018 and since then, it has been extensively studied. In this paper, we present a different way to obtain resolving structures in graphs in order to gain more insight into the study of edge resolving sets and resolving partitions. We define the edge partition dimension of a connected graph and bound it for graphs of given order and for graphs with given maximum degree. We obtain exact values of the edge partition dimension for multipartite graphs. Some relations between the edge partition dimension and partition dimension/edge metric dimension are also presented. Moreover, several open problems for further research are stated.
引用
收藏
页码：34 / 39
页数：6
相关论文
共 50 条
  • [21] A note on the partition dimension of Cartesian product graphs
    Yero, Ismael G.
    Rodriguez-Velazquez, Juan A.
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (07) : 3571 - 3574
  • [22] On fault-tolerant partition dimension of graphs
    Azhar, Kamran
    Zafar, Sohail
    Kashif, Agha
    Zahid, Zohaib
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2021, 40 (01) : 1129 - 1135
  • [23] On the partition dimension of two-component graphs
    Haryeni, D. O.
    Baskoro, E. T.
    Saputro, S. W.
    Baca, M.
    Semanicova-Fenovcikova, A.
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2017, 127 (05): : 755 - 767
  • [24] On 2-partition dimension of the circulant graphs
    Nadeem, Asim
    Kashif, Agha
    Zafar, Sohail
    Zahid, Zohaib
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2021, 40 (05) : 9493 - 9503
  • [25] On the partition dimension of two-component graphs
    D O Haryeni
    E T Baskoro
    S W Saputro
    M Bača
    A Semaničová-Feňovčíková
    Proceedings - Mathematical Sciences, 2017, 127 : 755 - 767
  • [26] Metric dimension and edge metric dimension of windmill graphs
    Singh, Pradeep
    Sharma, Sahil
    Sharma, Sunny Kumar
    Bhat, Vijay Kumar
    AIMS MATHEMATICS, 2021, 6 (09): : 9138 - 9153
  • [27] On graphs with the maximum edge metric dimension
    Zhu, Enqiang
    Taranenko, Andrej
    Shao, Zehui
    Xu, Jin
    DISCRETE APPLIED MATHEMATICS, 2019, 257 : 317 - 324
  • [28] Edge clique partition in (k, l)-graphs
    Jones, Atila A.
    Protti, Fabio
    Del-Vecchio, Renata R.
    DISCRETE APPLIED MATHEMATICS, 2022, 306 : 89 - 97
  • [29] Partition dimension of certain classes of series parallel graphs
    Mohan, Chris Monica
    Santhakumar, Samivel
    Arockiaraj, Micheal
    Liu, Jia-Bao
    THEORETICAL COMPUTER SCIENCE, 2019, 778 : 47 - 60
  • [30] Partition Dimension of Some Classes of Homogenous Disconnected Graphs
    Haryeni, Debi Oktia
    Baskoro, Edy Tri
    2ND INTERNATIONAL CONFERENCE OF GRAPH THEORY AND INFORMATION SECURITY, 2015, 74 : 73 - 78
12345