Second Zagreb index for fuzzy graphs and its application in mathematical chemistry

被引:18
作者
Islam, S. R. [1 ]
Pal, M. [1 ]
机构
[1] Vidyasagar Univ, Dept Appl Math Oceanol & Comp Programming, Midnapore 721102, India
来源
IRANIAN JOURNAL OF FUZZY SYSTEMS | 2023年 / 20卷 / 01期
关键词
Fuzzy graph; second Zagreb index; topological index; chemical graph; LINK PREDICTION; CONNECTIVITY;
D O I
10.22111/IJFS.2023.7350
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Zagreb index (ZI) of a crisp graph and also for a fuzzy graph (FG) is a very much useful tool in network theory, spectral graph theory, molecular chemistry and several fields of chemistry and mathematics. The second ZI is studied for FGs here. Bounds of this index are calculated for several FGs: path, star, cycle, complete FG, partial fuzzy subgraph, etc. For isomorphic FGs, it is shown that the value of this index is same. Bounds of this index for the Cartesian product, composition, join and union of two FGs are established. At the end of this article, an application of the index in mathematical chemistry is studied. For this, octane isomers are considered and analyzed the correlation between this index with some physico-chemical properties of octane isomers. This index's correlation coefficient (r) with acentric factor and entropy is determined for the linear curve fittings. Using the value of r, one can conclude that this index can help estimate the acentric factor and entropy with significant accuracy. Also, these outcomes declare the appropriateness of the index in QSPR research.
引用
收藏
页码:119 / 136
页数:18
相关论文
共 51 条
  • [1] Akram M., 2019, M POLAR FUZZY GRAPHS, DOI [10.1007/978-3-030-03751-2, DOI 10.1007/978-3-030-03751-2]
  • [2] Complex Pythagorean fuzzy threshold graphs with application in petroleum replenishment
    Akram, Muhammad
    Ahmad, Uzma
    Rukhsar
    Karaaslan, Faruk
    [J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (03) : 2125 - 2150
  • [3] q-Rung orthopair fuzzy graphs under Hamacher operators
    Akram, Muhammad
    Alsulami, Samirah
    Karaaslan, Faruk
    Khan, Ayesha
    [J]. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2021, 40 (01) : 1367 - 1390
  • [4] A new approach to compute measures of connectivity in rough fuzzy network models
    Akram, Muhammad
    Zafar, Fariha
    [J]. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2019, 36 (01) : 449 - 465
  • [5] Akram M, 2015, ITAL J PURE APPL MAT, P497
  • [6] Bipolar fuzzy graphs
    Akram, Muhammad
    [J]. INFORMATION SCIENCES, 2011, 181 (24) : 5548 - 5564
  • [7] Connectivity status of fuzzy graphs
    Binu, M.
    Mathew, Sunil
    Mordeson, J. N.
    [J]. INFORMATION SCIENCES, 2021, 573 : 382 - 395
  • [8] Cyclic Connectivity Index of Fuzzy Graphs
    Binu, M.
    Mathew, Sunil
    Mordeson, John N.
    [J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2021, 29 (06) : 1340 - 1349
  • [9] Wiener index of a fuzzy graph and application to illegal immigration networks
    Binu, M.
    Mathew, Sunil
    Mordeson, J. N.
    [J]. FUZZY SETS AND SYSTEMS, 2020, 384 : 132 - 147
  • [10] Connectivity index of a fuzzy graph and its application to human trafficking
    Binu, M.
    Mathew, Sunil
    Mordeson, J. N.
    [J]. FUZZY SETS AND SYSTEMS, 2019, 360 : 117 - 136