On the geometric-arithmetic index of a graph

被引：10
|
作者：
Chen, Yin [1 ]
Wu, Baoyindureng [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2019年 / 254卷
关键词：
Geometric-arithmetic index; Chromatic number; Clique number; CHROMATIC NUMBER; BOUNDS;
D O I：
10.1016/j.dam.2018.06.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Very recently, Aouchiche and Hansen gave an upper bound on the ratio of GA/chi of the geometric-arithmetic index GA(G) and the chromatic number chi(G) of a graph. Furthermore, they proposed several conjectures on the relation between geometric-arithmetic index and chromatic number, and clique number. In this note, we disprove four of those conjectures. In addition, we present a sufficient condition for an edge e is an element of E(G) with GA(G - e) < GA(G). (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：268 / 273
页数：6
相关论文
共 50 条
  • [31] Molecular graphs with extremal first geometric-arithmetic index
    Rostami, Mohammadreza
    Ghorbani, Modjtaba
    ARS COMBINATORIA, 2017, 135 : 235 - 242
  • [32] Study on geometric-arithmetic, arithmetic-geometric and Randić indices of graphs
    Das, Kinkar Chandra
    Huh, Da-yeon
    Bera, Jayanta
    Mondal, Sourav
    DISCRETE APPLIED MATHEMATICS, 2025, 360 : 229 - 245
  • [33] On the spread of the geometric-arithmetic matrix of graphs
    Rather, Bilal A.
    Aouchiche, M.
    Pirzada, S.
    AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2022, 19 (02) : 146 - 153
  • [34] Some Mathematical Properties of the Geometric-Arithmetic Index/Coindex of Graphs
    Stankov, S.
    Matejic, M.
    Milovanovic, I
    Milovanovic, E.
    FILOMAT, 2021, 35 (15) : 5045 - 5057
  • [35] The Geometric-Arithmetic index of trees with a given total domination number
    Bermudo, Sergio
    Hasni, Roslan
    Movahedi, Fateme
    Napoles, Juan E.
    DISCRETE APPLIED MATHEMATICS, 2024, 345 : 99 - 113
  • [36] A Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes
    Yarahmadi, Zahra
    IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 2011, 2 (02): : 101 - 108
  • [37] Extremal graphs for the geometric-arithmetic index with given minimum degree
    Divnic, Tomica
    Milivojevic, Milica
    Pavlovic, Ljiljana
    DISCRETE APPLIED MATHEMATICS, 2014, 162 : 386 - 390
  • [38] The minimum value of geometric-arithmetic index of graphs with minimum degree 2
    Mahdi Sohrabi-Haghighat
    Mohammadreza Rostami
    Journal of Combinatorial Optimization, 2017, 34 : 218 - 232
  • [39] Upper bound for the geometric-arithmetic index of trees with given domination number
    Bermudo, Sergio
    DISCRETE MATHEMATICS, 2023, 346 (01)
  • [40] The minimum value of geometric-arithmetic index of graphs with minimum degree 2
    Sohrabi-Haghighat, Mahdi
    Rostami, Mohammadreza
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2017, 34 (01) : 218 - 232
12345