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  • ISSN 1006-3080
  • CN 31-1691/TQ

基于字典序乘积下广义和连通度指标的上下界

李志豪 朱焱

李志豪, 朱焱. 基于字典序乘积下广义和连通度指标的上下界[J]. 华东理工大学学报(自然科学版), 2022, 48(3): 405-410. doi: 10.14135/j.cnki.1006-3080.20210204001
引用本文: 李志豪, 朱焱. 基于字典序乘积下广义和连通度指标的上下界[J]. 华东理工大学学报(自然科学版), 2022, 48(3): 405-410. doi: 10.14135/j.cnki.1006-3080.20210204001
LI Zhihao, ZHU Yan. Sharp Bounds on General Sum-Connectivity Index Based on Lexicographic Product[J]. Journal of East China University of Science and Technology, 2022, 48(3): 405-410. doi: 10.14135/j.cnki.1006-3080.20210204001
Citation: LI Zhihao, ZHU Yan. Sharp Bounds on General Sum-Connectivity Index Based on Lexicographic Product[J]. Journal of East China University of Science and Technology, 2022, 48(3): 405-410. doi: 10.14135/j.cnki.1006-3080.20210204001

基于字典序乘积下广义和连通度指标的上下界

doi: 10.14135/j.cnki.1006-3080.20210204001
基金项目: 国家自然科学基金(11671135)
详细信息
    作者简介:

    李志豪(1996-),男,河南省驻马店人,硕士生,研究方向为图论。E-mail:15216879521@163.com

    通讯作者:

    朱 焱(1984—),E-mail:zhuygraph@ecust.edu.cn

  • 中图分类号: O157

Sharp Bounds on General Sum-Connectivity Index Based on Lexicographic Product

  • 摘要: 对于图$ G $,令$ E\left(G\right) $$ {d}_{G}\left(v\right) $分别表示$ G $的边集和顶点$ v $的度。对于边$ e=uv $,定义广义和连通度指标$ {\chi }_{\alpha }\left(e\right)={({d}_{G}\left(u\right)+{d}_{G}(v\left)\right)}^{\alpha } $,其中$ \alpha $为任意实数。在对两个简单的连通图$ G $H做乘积之前,先对其中一个图H进行$ S, R, Q, T $4种运算,运算后的图记为$ F\left(H\right) $(其中$ F\in \{S, R, Q, T\} $),再对图$ G $$ F\left(H\right) $做字典序乘积,给出了基于字典序乘积下图的广义和连通度的指标上下界,并且这些界都是最好的。

     

  • 图  1  $F\in \{S, R, Q, T\} $F(P6)的4种运算

    Figure  1.  Four operations of F(P6) ${\rm{ at}} \;F\in \{S, R, Q, T\} $

    图  2  $ F\in \{S, R, Q, T\} $时图P3[P3]的4种运算

    Figure  2.  Four operations on graph P3[P3] at F ϵ {S,R,Q,T}

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出版历程
  • 收稿日期:  2021-02-04
  • 网络出版日期:  2021-06-25
  • 刊出日期:  2022-06-29

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