Monitoring Edge-Geodetic Numbers of Some Networks

被引：3
|
作者：
Zhang, Yingying [1 ]
Wang, Fanfan [1 ]
Yang, Chenxu [2 ]
机构：
[1] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China
[2] Qinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
来源：
JOURNAL OF INTERCONNECTION NETWORKS | 2024年
关键词：
Distance; monitoring edge-geodetic set; monitoring edge-geodetic number; networks; TOPOLOGICAL PROPERTIES;
D O I：
10.1142/S0219265924500014
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Motivated by the problem of network monitoring, Foucaud, Krishna and Ramasubramony Sulochana introduced the concept of monitoring edge-geodetic set and a related graph invariant. A monitoring edge-geodetic set (MEG-set for short) is a set such that the removal of any edge changes the distance between some pair of vertices in the set. The minimum size of the monitoring edge-geodetic set is called the monitoring edge-geodetic number. In this paper, we study the monitoring edge-geodetic numbers of some well-known networks, including folded hypercube, folded n-cube, prism graph, anti-prism graph, Jahangir graph and windmill graphs.
引用
收藏
页数：14
相关论文
共 50 条
  • [1] Monitoring edge-geodetic numbers of convex polytopes and four networks
    Tan, Ao
    Li, Wen
    Wang, Xiumin
    Li, Xin
    [J]. INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS, 2023, 38 (04) : 301 - 312
  • [2] Monitoring Edge-Geodetic Numbers of Mycielskian Graph Classes
    Li, Xin
    Li, Wen
    Tan, Ao
    He, Mengmeng
    Chen, Weizhen
    [J]. JOURNAL OF INTERCONNECTION NETWORKS, 2024,
  • [3] Monitoring Edge-Geodetic Sets in Graphs
    Foucaud, Florent
    Narayanan, Krishna
    Sulochana, Lekshmi Ramasubramony
    [J]. ALGORITHMS AND DISCRETE APPLIED MATHEMATICS, CALDAM 2023, 2023, 13947 : 245 - 256
  • [4] Monitoring edge-geodetic sets: Hardness and graph products
    Haslegrave, John
    [J]. DISCRETE APPLIED MATHEMATICS, 2023, 340 : 79 - 84
  • [5] Monitoring Edge-Geodetic Sets in Graphs: Extremal Graphs, Bounds, Complexity
    Foucaud, Florent
    Marcille, Pierre-Marie
    Myint, Zin Mar
    Sandeep, R. B.
    Sen, Sagnik
    Taruni, S.
    [J]. ALGORITHMS AND DISCRETE APPLIED MATHEMATICS, CALDAM 2024, 2024, 14508 : 29 - 43
  • [6] On the Monitoring-Edge-Geodetic Numbers of Line Graphs
    Bao, Gemaji
    Yang, Chenxu
    Ma, Zhiqiang
    Ji, Zhen
    Xu, Xin
    Qin, Peiyao
    [J]. JOURNAL OF INTERCONNECTION NETWORKS, 2023,
  • [7] On the edge geodetic and edge geodetic domination numbers of a graph
    Samodivkin, Vladimir
    [J]. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2020, 5 (01) : 41 - 54
  • [8] Monitoring-edge-geodetic sets in product networks
    Xu, Xin
    Yang, Chenxu
    Bao, Gemaji
    Zhang, Ayun
    Shao, Xuan
    [J]. INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS, 2024, 39 (02) : 264 - 277
  • [9] Distance-edge-monitoring numbers of some related pseudo wheel networks
    Yang, Chenxu
    Deng, Xingchao
    Ji, Zhen
    Li, Wen
    [J]. INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS, 2024, 39 (03) : 362 - 378
  • [10] Monitoring-edge-geodetic numbers of radix triangular mesh and Sierpiński graphs
    Ma, Rongrong
    Ji, Zhen
    Yao, Yifan
    Lei, Yalong
    [J]. INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS, 2024, 39 (03) : 353 - 361
12345