INVERSE DEGREE, RANDIC INDEX AND HARMONIC INDEX OF GRAPHS

被引：16
|
作者：
Das, Kinkar Ch. [1 ]
Balachandran, Selvaraj [2 ]
Gutman, Ivan [3 ]
机构：
[1] Sungkyunkwan Univ, Dept Math, Suwon 440746, South Korea
[2] SASTRA Univ, Sch Humanities & Sci, Dept Math, Thanjavur, India
[3] Univ Kragujevac, Fac Sci, POB 60, Kragujevac 34000, Serbia
来源：
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2017年 / 11卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
Degree (of vertex); Inverse degree; Randic index; Harmonic index; TOPOLOGICAL INDEXES; DIAMETER; CONNECTIVITY;
D O I：
10.2298/AADM1702304D
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a graph with vertex set V and edge set E. Let d(i) be the degree of the vertex v(i) of G. The inverse degree, Randic index, and harmonic index of G are defined as I D = Sigma v(i)epsilon V-1/di, R = Sigma v(i)v(j) epsilon E 1/root d(i)d(j) , and H = Sigma v(i)v(j) epsilon E 2/(d(i) + d(j)), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.
引用
收藏
页码：304 / 313
页数：10
相关论文
共 50 条
  • [41] On the Randic index
    Delorme, C
    Favaron, O
    Rautenbach, D
    DISCRETE MATHEMATICS, 2002, 257 (01) : 29 - 38
  • [42] The Harmonic Index for Bicyclic Graphs
    Zhong, Lingping
    Xu, Kexiang
    UTILITAS MATHEMATICA, 2013, 90 : 23 - 32
  • [43] NOTES ON THE HARMONIC INDEX OF GRAPHS
    Zheng, Yirong
    Lv, Jian-Bo
    LI, Jianxi
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2022, 52 (06) : 2247 - 2255
  • [44] The Harmonic Index on Unicyclic Graphs
    Zhong, Lingping
    ARS COMBINATORIA, 2012, 104 : 261 - 269
  • [45] The harmonic index on bicyclic graphs
    Zhu, Yan
    Chang, Renying
    Wei, Xiang
    ARS COMBINATORIA, 2013, 110 : 97 - 104
  • [46] Maximum Randic Index on Unicyclic Graphs with k Pendant Vertices
    Li, Fan
    Lu, Mei
    ARS COMBINATORIA, 2014, 116 : 385 - 394
  • [47] On the harmonic index in cactus graphs
    Rad, Nader Jafari
    Hasni, Roslan
    Kamarulhaili, Hailiza
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2025, 17 (01)
  • [48] The Harmonic Index of Some Graphs
    Jianxi Li
    Jian-Bo Lv
    Yang Liu
    Bulletin of the Malaysian Mathematical Sciences Society, 2016, 39 : 331 - 340
  • [49] Harmonic index of dense graphs
    Liu, Jianxi
    ARS COMBINATORIA, 2015, 120 : 293 - 304
  • [50] General Randic index of unicyclic graphs with given girth and diameter
    Vetrik, Tomas
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2022, 15 (09)
12345