基于强乘积运算下图的广义和连通度指标上下界

doi:10.15960/j.cnki.issn.1007-6093.2024.01.012

运筹学学报 ›› 2024, Vol. 28 ›› Issue (1): 141-152.doi: 10.15960/j.cnki.issn.1007-6093.2024.01.012

基于强乘积运算下图的广义和连通度指标上下界

李志豪¹, 朱焱¹^,*()

1. 华东理工大学数学学院, 上海 200237

收稿日期:2020-12-24 出版日期:2024-03-15 发布日期:2024-03-15
通讯作者: 朱焱 E-mail:zhuygraph@ecust.edu.cn
基金资助:
国家自然科学基金(11671135)

The sharp bounds on general sum-connectivity index of graphs for operations based on strong product

Zhihao LI¹, Yan ZHU¹^,*()

1. School of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received:2020-12-24 Online:2024-03-15 Published:2024-03-15
Contact: Yan ZHU E-mail:zhuygraph@ecust.edu.cn

摘要/Abstract

摘要：

对于图$G$, 令$E(G)$表示$G$的边集, 令$V(G)$表示$G$的点集, $d_G(v)$表示$v$的度。对于边$e=uv$, 定义广义和连通度指标$\chi_\alpha(e)=(d_G(u)+d_G(v))^\alpha$, 其中$\alpha$为任一实数。本文先介绍了图的$S, R, Q, T$四种运算, 然后给出了四种运算下的强乘积, 并利用最大度最小度确定了其四种图的广义和连通度指标的上下界。

关键词: 广义和连通度指标, 强乘积, 四种运算, F-和

Abstract:

For a graph $G$, the edge set of graph $G$ denoted by $E(G)$, the vertex set of graph $G$ denoted by $V(G)$, let $d_G (v)$ denote the degree of $v$. For an edge $e=uv$, the general sum-connectivity index $\chi_\alpha(e)=(d_G(u)+d_G(v))^\alpha$, in which $\alpha$ is any real number. In current paper, we introduce firstly the four operations($S, R, Q, T$) of the graph, then give the strong product under the four operations, and determine the upper and lower bounds of the general sum-connectivity index of the four graphs by using the maximum and minimum degrees.

Key words: general sum-connectivity index, strong product, four new operations, F-sum

中图分类号:

O157

李志豪, 朱焱. 基于强乘积运算下图的广义和连通度指标上下界[J]. 运筹学学报, 2024, 28(1): 141-152.

Zhihao LI, Yan ZHU. The sharp bounds on general sum-connectivity index of graphs for operations based on strong product[J]. Operations Research Transactions, 2024, 28(1): 141-152.

图/表 2

参考文献 17

1	Wiener H . Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69 (1): 17- 20. doi: 10.1021/ja01193a005
2	Gutman I , Trinajstić N . Graph theory and molecular orbitals, total $\pi$-electron energy of alternant hydrocarbons[J]. Chemical Physics Letters, 1972, 17 (4): 535- 538. doi: 10.1016/0009-2614(72)85099-1
3	Deng H , Sarala D , Ayyaswamy S K , et al. The Zagreb indices of four operations on graphs[J]. Applied Mathematics and Computation, 2016, 275, 422- 431. doi: 10.1016/j.amc.2015.11.058
4	Li X , Zheng J . A unified approach to the extremal trees for different indices[J]. Match Communications in Mathematical & in Computer Chemistry, 2005, 54, 195- 208.
5	Zhou B , Trinajstić N . On a novel connectivity index[J]. Journal of Mathematical Chemistry, 2009, 46, 1252- 1270. doi: 10.1007/s10910-008-9515-z
6	Zhou B , Trinajstić N . On general sum-connectivity index[J]. Journal of Mathematical Chemistry, 2010, 47, 210- 218. doi: 10.1007/s10910-009-9542-4
7	秦倩楠, 邵燕灵. 三圈图的极小广义和连通指数[J]. 运筹学学报, 2018, 22 (1): 142- 150.
8	Cvetkovic D M , Doob M , Sachs H . Spectra of Graphs: Theory and Applications[M]. New York: Academic, 1980.
9	Yan W , Yang B Y , Yeh Y N . The behavior of Wiener indices and polynomials of graphs under five graph decorations[J]. Applied Mathematics Letters, 2007, 20, 290- 295. doi: 10.1016/j.aml.2006.04.010
10	Eliasi M , Taeri B . Four new sums of graphs and their Wiener indices[J]. Discrete Applied Mathematics, 2009, 157 (4): 794- 803. doi: 10.1016/j.dam.2008.07.001
11	De N , Nayeem S M A , Pal A . F-index of some graph operations[J]. Discrete Mathematics Algorithms and Applications, 2016, 8 (2): 1650025- 1650025. doi: 10.1142/S1793830916500257
12	Onagh B N . The harmonic index of graphs based on some operations related to the lexicographic product[J]. Mathematical Sciences, 2019, 13, 165- 174. doi: 10.1007/s40096-019-0287-3
13	Akhter S , Imran M . The sharp bounds on general sum-connectivity index of four operations on graphs[J]. Journal of Inequalities and Applications, 2016, 2016, 241. doi: 10.1186/s13660-016-1186-x
14	Ahmad M , Saeed M , Javaid M , et al. Exact formula and improved bounds for general sum-connectivity index of graph-operations[J]. IEEE Access, 2019, 167290- 167299.
15	Du Z , Zhou B , Trinajstić N . Minimum general sum-connectivity index of unicyclic graphs[J]. Journal of Mathematical Chemistry, 2010, 48, 697- 703. doi: 10.1007/s10910-010-9702-6
16	Tache R M . General sum-connectivity index with $\alpha\geq-1$ for bicyclic graphs[J]. Match Communications in Mathematical and in Computer Chemistry, 2014, 72, 761- 774.
17	Tomescua I , Kanwal S . Ordering trees having small general sum-connectivity index[J]. Match Communications in Mathematical and in Computer Chemistry, 2013, 69, 535- 548.

[1]	余桂东, 刘珍珍, 王礼想, 李青. 可迹图的一些新充分条件[J]. 运筹学学报, 2024, 28(1): 131-140.
[2]	何常香, 王文燕, 刘乐乐. 关于赋权非正则图的A_α特征值和特征向量[J]. 运筹学学报, 2024, 28(1): 121-130.
[3]	苏雪丽, 李晓辉, 刘岩. 二维四角网格图的反馈数上界的改进[J]. 运筹学学报, 2024, 28(1): 153-158.
[4]	刘乐乐, 宁博. 谱图理论中的未解决问题[J]. 运筹学学报, 2023, 27(4): 33-60.
[5]	郝建修. 关于网络的控制数的几点注记[J]. 运筹学学报, 2023, 27(3): 185-190.
[6]	张杰, 姬燕. 单圈图的Steiner Wiener指数的极值问题[J]. 运筹学学报, 2023, 27(3): 178-184.
[7]	袁玲, 王文环. 不含偶圈(n, m)-图匹配多项式的最大根[J]. 运筹学学报, 2023, 27(3): 150-158.
[8]	崔福祥, 杨超, 叶宏波, 姚兵. 图的邻点全和可区别全染色[J]. 运筹学学报, 2023, 27(1): 149-158.
[9]	王蝶, 康丽英. 一般超图的张量谱性质[J]. 运筹学学报, 2023, 27(1): 138-148.
[10]	卜月华, 张恒. 平面图的强边染色[J]. 运筹学学报, 2022, 26(2): 111-127.
[11]	余桂东, 阮征, 舒阿秀. k圈图的最大Laplace分离度[J]. 运筹学学报, 2022, 26(2): 137-142.
[12]	王银玲, 韩鑫, 邵欣欣. 关于带运输的单机调度在线问题的研究[J]. 运筹学学报, 2022, 26(1): 125-133.
[13]	李春梅, 王治文. Δ(G)=5的2-连通外平面图的邻点可区别全染色[J]. 运筹学学报, 2021, 25(4): 120-126.
[14]	董艳侠, 薛涛, 张广. 广义de Bruijn有向图的k-元控制集[J]. 运筹学学报, 2021, 25(2): 127-134.
[15]	刘瑶. 带松弛条件的图的强边着色[J]. 运筹学学报, 2021, 25(2): 115-126.

基于强乘积运算下图的广义和连通度指标上下界

The sharp bounds on general sum-connectivity index of graphs for operations based on strong product

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 2

参考文献 17

相关文章 15

编辑推荐

Metrics

本文评价