Strong Domination Index in Fuzzy Graphs

被引：0
|
作者：
Nair, Kavya R. [1 ]
Sunitha, Muraleedharan Shetty [1 ]
机构：
[1] Natl Inst Technol, Dept Math, Calicut 673601, India
来源：
FUZZY INFORMATION AND ENGINEERING | 2024年 / 16卷 / 01期
关键词：
strong domination degree; strong domination regular fuzzy graph (FG); strong domination index; upper strong domination number; strong irredundance number; strong upper irredundance number; strong independent domination number; strong independence number; r-partite FG; TOPOLOGICAL INDEXES; INDEPENDENCE;
D O I：
10.26599/FIE.2023.9270028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, a novel idea of domination degree and index are defined in a fuzzy graph (FG) using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Methods to obtain an MSDS containing a particular vertex are discussed in the article. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of an FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle, and fuzzy stars. Bounds involving the SDD and SDI are also obtained. Applications for SDD of a vertex is also provided.
引用
收藏
页码：1 / 23
页数：23
相关论文
共 50 条
  • [21] Domination in Pythagorean fuzzy graphs
    Sadegh Banitalebi
    Rajab Ali Borzooei
    Granular Computing, 2023, 8 (5) : 959 - 966
  • [22] Domination in Bipolar Fuzzy Graphs
    Karunambigai, M. G.
    Akram, M.
    Palanivel, K.
    Sivasankar, S.
    2013 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ - IEEE 2013), 2013,
  • [23] On (r; s)-Fuzzy Domination in Fuzzy Graphs
    Arumugam, S.
    Bhutani, Kiran
    Sathikala, L.
    NEW MATHEMATICS AND NATURAL COMPUTATION, 2016, 12 (01) : 1 - 10
  • [24] On Restrained Strong Resolving Domination in Graphs
    Sumaoy, Helyn C.
    Rara, Helen M.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2021, 14 (04): : 1367 - 1378
  • [25] Strong Resolving Hop Domination in Graphs
    Mohamad, Jerson S.
    Rara, Helen M.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, 16 (01): : 131 - 143
  • [26] On Movable Strong Resolving Domination in Graphs
    Sumaoy, Helyn C.
    Rara, Helen M.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (03): : 1201 - 1210
  • [27] On the strong Roman domination number of graphs
    Alvarez-Ruiz, M. P.
    Mediavilla-Gradolph, T.
    Sheikholeslami, S. M.
    Valenzuela-Tripodoro, J. C.
    Yero, I. G.
    DISCRETE APPLIED MATHEMATICS, 2017, 231 : 44 - 59
  • [28] Weak and strong domination on some graphs
    Durgun, Derya Dogan
    Kurt, Berna Lokcu
    RAIRO-OPERATIONS RESEARCH, 2022, 56 (04) : 2305 - 2314
  • [29] The inverse strong nonsplit domination in graphs
    Packiarani, D. Kiruba
    Mary, Y. Therese Sunitha
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2021, 13 (06)
  • [30] Weak and strong domination in thorn graphs
    Durgun, Derya Dogan
    Lokcu, Berna
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (04)
12345