The connectivity and the Harary index of a graph

被引：30
|
作者：
Li, Xiao-Xin [1 ,2 ]
Fan, Yi-Zheng [2 ]
机构：
[1] Chizhou Univ, Dept Math, Chizhou 247000, Peoples R China
[2] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2015年 / 181卷
基金：
中国国家自然科学基金;
关键词：
Graph; Harary index; Cut vertex; Vertex connectivity; Edge connectivity; HYPER-WIENER; MATRIX;
D O I：
10.1016/j.dam.2014.08.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with the maximum Harary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In addition we also characterize the extremal graphs with the second maximum Harary index among all graphs with given vertex connectivity. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：167 / 173
页数：7
相关论文
共 50 条
  • [1] On the Harary Energy and Harary Estrada Index of a Graph
    Gungor, A. Dilek
    Cevik, A. Sinan
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2010, 64 (01) : 281 - 296
  • [2] On the Harary index of graph operations
    Kinkar C Das
    Kexiang Xu
    Ismail Naci Cangul
    Ahmet Sinan Cevik
    Ante Graovac
    Journal of Inequalities and Applications, 2013
  • [3] On the Harary index of graph operations
    Das, Kinkar C.
    Xu, Kexiang
    Cangul, Ismail Naci
    Cevik, Ahmet Sinan
    Graovac, Ante
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [4] Wiener index, Harary index and graph properties
    Feng, Lihua
    Zhu, Xiaomin
    Liu, Weijun
    DISCRETE APPLIED MATHEMATICS, 2017, 223 : 72 - 83
  • [5] THE HARARY INDEX OF A GRAPH UNDER PERTURBATION
    He, Chang-Xiang
    Chen, Ping
    Wu, Bao-Feng
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2010, 2 (02) : 247 - 255
  • [6] Role of Graph Theory to Facilitate Landscape Connectivity: Subdivision of a Harary Graph
    Arif, Khalid
    Afzal, Zeeshan
    Nadeem, Muhammad
    Ahmad, Bilal
    Mahmood, Azhar
    Iqbal, Munawar
    Nazir, Arif
    POLISH JOURNAL OF ENVIRONMENTAL STUDIES, 2018, 27 (03): : 993 - 999
  • [7] HARARY INDEX OF THE k-TH POWER OF A GRAPH
    Su, Guifu
    Xiong, Liming
    Gutman, Ivan
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2013, 7 (01) : 94 - 105
  • [8] On Harary Matrix, Harary Index and Harary Energy
    Cui, Zhihui
    Liu, Bolian
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2012, 68 (03) : 815 - 823
  • [9] Some extremal properties of the multiplicatively weighted Harary index of a graph
    Li, Shuchao
    Zhang, Huihui
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2016, 31 (03) : 961 - 978
  • [10] Distance-based graph invariants of trees and the Harary index
    Wagner, Stephan
    Wang, Hua
    Zhang, Xiao-Dong
    FILOMAT, 2013, 27 (01) : 41 - 50
12345