Sharp bounds for the second Zagreb index of unicyclic graphs

被引：51
|
作者：
Yan, Zheng [1 ]
Liu, Huiqing [1 ]
Liu, Heguo [1 ]
机构：
[1] Hubei Univ, Sch Math & Comp Sci, Wuhan 430062, Peoples R China
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2007年 / 42卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Zagreb index; unicyclic graph; pendant vertex;
D O I：
10.1007/s10910-006-9132-7
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
The second Zagreb index M-2( G) of a ( molecule) graph G is the sum of the weights d( u) d( v) of all edges uv of G, where d( u) denotes the degree of the vertex u. In this paper, we give sharp upper and lower bounds on the second Zagreb index of unicyclic graphs with n vertices and k pendant vertices. From which, U-n-3(n) and C-n have the maximum and minimum the second Zagreb index among all unicyclic graphs with n vertices, respectively.
引用
收藏
页码：565 / 574
页数：10
相关论文
共 50 条
  • [41] Extremal Zagreb indices of unicyclic graphs
    Chen, Shubo
    Zhou, Houqing
    UTILITAS MATHEMATICA, 2019, 113 : 311 - 318
  • [42] Computing Bounds for Second Zagreb Coindex of Sum Graphs
    Javaid, Muhammad
    Ibraheem, Muhammad
    Ahmad, Uzma
    Zhu, Q.
    Mathematical Problems in Engineering, 2021, 2021
  • [43] Computing Bounds for Second Zagreb Coindex of Sum Graphs
    Javaid, Muhammad
    Ibraheem, Muhammad
    Ahmad, Uzma
    Zhu, Q.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021
  • [44] Bounds on the PI index of unicyclic and bicyclic graphs with given girth
    Ma, Gang
    Bian, Qiuju
    Wang, Jianfeng
    DISCRETE APPLIED MATHEMATICS, 2017, 230 : 156 - 161
  • [45] On general reduced second Zagreb index of graphs
    Horoldagva, Batmend
    Buyantogtokh, Lkhagva
    Das, Kinkar Ch
    Lee, Sang-Gu
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2019, 48 (04): : 1046 - 1056
  • [46] Reduced second Zagreb index of product graphs
    De, N.
    NANOSYSTEMS-PHYSICS CHEMISTRY MATHEMATICS, 2020, 11 (02): : 131 - 137
  • [47] On General Reduced Second Zagreb Index of Graphs
    Buyantogtokh, Lkhagva
    Horoldagva, Batmend
    Das, Kinkar Chandra
    MATHEMATICS, 2022, 10 (19)
  • [48] Sharp upper bounds for Zagreb indices of bipartite graphs with a given diameter
    Li, Shuchao
    Zhang, Minjie
    APPLIED MATHEMATICS LETTERS, 2011, 24 (02) : 131 - 137
  • [49] Sharp upper bounds for Zagreb indices of bipartite graphs with a given diameter
    Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
    不详
    Appl Math Lett, 2 (131-137):
  • [50] Sharp Bounds of First Zagreb Coindex for F-Sum Graphs
    Javaid, Muhammad
    Ibraheem, Muhammad
    Ahmad, Uzma
    Liu, Jia-Bao
    JOURNAL OF MATHEMATICS, 2021, 2021
12345