A lower bound for the harmonic index of a graph with minimum degree at least two

被引：61
|
作者：
Wu, Renfang [1 ]
Tang, Zikai [1 ]
Deng, Hanyuan [1 ]
机构：
[1] Hunan Normal Univ, Minist Educ China, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
来源：
FILOMAT | 2013年 / 27卷 / 01期
关键词：
Graph; the harmonic index; the minimum degree;
D O I：
10.2298/FIL1301051W
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The harmonic index H(G) of a graph G is defined as the sum of the weights 2/ d(u)+ d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. We give a best possible lower bound for the harmonic index of a graph (a triangle-free graph, respectively) with minimum degree at least two and characterize the extremal graphs.
引用
收藏
页码：51 / 55
页数：5
相关论文
共 50 条
  • [1] A Lower Bound for the Harmonic Index of a Graph with Minimum Degree at Least Three
    Cheng, Minghong
    Wang, Ligong
    FILOMAT, 2016, 30 (08) : 2249 - 2260
  • [2] The minimum value of the harmonic index for a graph with the minimum degree two
    Deng, Hanyuan
    Balachandran, S.
    Balachandar, S. Raja
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (03)
  • [3] On The Harmonic Index and The Minimum Degree of A Graph
    Chang, Renying
    Zhu, Yan
    ROMANIAN JOURNAL OF INFORMATION SCIENCE AND TECHNOLOGY, 2012, 15 (04): : 335 - 343
  • [4] The linear programming approach to the harmonic index of a graph with minimum degree at least three
    Chang, Renying
    Zhu, Yan
    ARS COMBINATORIA, 2018, 141 : 85 - 92
  • [5] An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree
    Hattingh, Johannes H.
    Joubert, Ernst J.
    DISCRETE APPLIED MATHEMATICS, 2009, 157 (13) : 2846 - 2858
  • [6] An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree
    Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, United States
    不详
    Discrete Appl Math, 13 (2846-2858):
  • [7] A Note on the Upper Bound for the Paired-Domination Number of a Graph with Minimum Degree At Least Two
    Huang, Shenwei
    Shan, Erfang
    NETWORKS, 2011, 57 (02) : 115 - 116
  • [8] A lower bound for the smallest uniquely hamiltonian planar graph with minimum degree three
    Klocker, Benedikt
    Fleischner, Herbert
    Raidl, Guenther R.
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 380
  • [9] A lower bound for the smallest uniquely hamiltonian planar graph with minimum degree three
    Klocker B.
    Fleischner H.
    Raidl G.R.
    Applied Mathematics and Computation, 2020, 380
  • [10] On a Conjecture of the Harmonic Index and the Minimum Degree of Graphs
    Sun, Xiaoling
    Gao, Yubin
    Du, Jianwei
    Xu, Lan
    FILOMAT, 2018, 32 (10) : 3435 - 3441
12345