Unicycle graphs with extremal Merrifield-Simmons index

被引：15
|
作者：
Wang, Hongzhuan [1 ]
Hua, Hongbo [1 ]
机构：
[1] Huaiyin Inst Technol, Dept Comp Sci, Jiangsu 223000, Peoples R China
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2008年 / 43卷 / 01期
关键词：
unicycle graph; Merrifield - Simmons index; girth;
D O I：
10.1007/s10910-006-9188-4
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
The Merrifield - Simmons index f (G) of a (molecular) graph G is defined as the number of subsets of the vertex set, in which any two vertices are non-adjacent, i.e., the number of independent-vertex sets of G. By U(n, k) we denote the set of unicycle graphs in which the length of its unique cycle is k. In this paper, we investigate the Merrifield - Simmons index f (G) for an unicycle graph G in U(n, k). Unicycle graphs with the largest or smallest Merrifield - Simmons index are uniquely determined.
引用
收藏
页码：202 / 209
页数：8
相关论文
共 50 条
  • [31] On the Merrifield-Simmons index of trees
    Li, XL
    Zhao, HX
    Gutman, I
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2005, 54 (02) : 389 - 402
  • [32] The Hosoya index and the Merrifield-Simmons index
    Huang, Yufeng
    Shi, Lingsheng
    Xu, Xingyu
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2018, 56 (10) : 3136 - 3146
  • [33] Largest Hosoya Index and Smallest Merrifield-Simmons Index in Tricyclic Graphs
    Liu, Yan
    Zhuang, Wei
    Liang, Zefang
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2015, 73 (01) : 195 - 224
  • [34] The Merrifield-Simmons Index and Hosoya Index of C(n, k, λ) Graphs
    Dai, Shaojun
    Zhang, Ruihai
    JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [35] On conjecture of Merrifield-Simmons index
    Das, Kinkar Chandra
    Elumalai, Suresh
    Ghosh, Arpita
    Mansour, Toufik
    DISCRETE APPLIED MATHEMATICS, 2021, 288 (288) : 211 - 217
  • [36] EXTREMAL VALUES OF MERRIFIELD-SIMMONS INDEX FOR TREES WITH TWO BRANCHING VERTICES
    Cruz, Roberto
    Marin, Carlos Alberto
    Rada, Juan
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2018, 42 (01): : 97 - 106
  • [37] Algorithmic generation of molecular graphs with large Merrifield-Simmons index
    Tichy, Robert F.
    Wagner, Stephan G.
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2008, 59 (01) : 239 - 252
  • [38] On the Hosoya index and the Merrifield-Simmons index of graphs with a given clique number
    Xu, Kexiang
    APPLIED MATHEMATICS LETTERS, 2010, 23 (04) : 395 - 398
  • [39] On the Merrifield-Simmons index and Hosoya index of bicyclic graphs with a given girth
    Sun, Renbin
    Zhu, Zhongxun
    Tan, Liansheng
    ARS COMBINATORIA, 2012, 103 : 465 - 478
  • [40] Some graphs with minimum Hosoya Index and maximum Merrifield-Simmons
    Pan, Xiang-Feng
    Xu, Jun-Ming
    Yang, Chao
    Zhou, Min-Jie
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2007, 57 (01) : 235 - 242
12345