• ISSN 1006-3080
• CN 31-1691/TQ

 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.
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.

• 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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