仙人掌图的Steiner (n－1)-Wiener指标与Steiner 3-Wiener指标

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (3): 161-167.

仙人掌图的Steiner (n－1)-Wiener指标与Steiner 3-Wiener指标

尹月琴, 吴帆, 安新慧^*

新疆大学数学与系统科学学院, 新疆乌鲁木齐 830046

收稿日期:2024-01-31 出版日期:2026-06-28 发布日期:2026-06-30
通讯作者: 安新慧(1978-),女,甘肃陇西人,博士,副教授.Email:xjaxh@163.com
基金资助:
国家自然科学基金(11801487)

Steiner (n－1)-Wiener and Steiner 3-Wiener indices of cacti

YIN Yue-qin, WU Fan, AN Xin-hui

School of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Received:2024-01-31 Online:2026-06-28 Published:2026-06-30

摘要/Abstract

摘要： 当2≤k≤n－1时,一个连通图G的Steiner k-Wiener指标表示顶点集V(G)中所有k元子集S的Steiner距离之和.研究了仙人掌图的Steiner(n－1)-Wiener指标的界和Steiner 3-Wiener指标的界,并给出了相应的极图.

关键词: 仙人掌图, Steiner(n－1)-Wiener指标, Steiner 3-Wiener指标

Abstract: For 2≤k≤n－1, the Steiner k-Wiener index of a connected graphG is the sum of Steiner distances of all k-subsets S of V(G). The bounds of the Steiner (n－1)-Wiener index and the bound of the Steiner 3-Wiener index of the cactus are studied and the corresponding Extremal graphs are given.

Key words: cacti, Steiner(n－1)-Wiener index, Steiner 3-Wiener index

中图分类号:

O157.5

尹月琴, 吴帆, 安新慧. 仙人掌图的Steiner (n－1)-Wiener指标与Steiner 3-Wiener指标[J]. 兰州理工大学学报, 2026, 52(3): 161-167.

YIN Yue-qin, WU Fan, AN Xin-hui. Steiner (n－1)-Wiener and Steiner 3-Wiener indices of cacti[J]. Journal of Lanzhou University of Technology, 2026, 52(3): 161-167.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: https://journal.lut.edu.cn/CN/

https://journal.lut.edu.cn/CN/Y2026/V52/I3/161

参考文献

[1] BONDY J A,MURTY U S R.Graph theory[M].London:Springer London,2008.
[2] CHARTRAND G,OELLERMANN O R,TIAN S L,et al.Steiner distance in graphs[J].Časopis Pro Pěstování Matematiky,1989,114(4):399-410.
[3] GUTMAN I,LI X L,MAO Y P.The steiner Wiener index of a graph[J].DiscussionesMathematicae Graph Theory,2016,36(2):455-465.
[4] DOBRYNIN A A,ENTRINGER R,GUTMAN I.Wiener index of trees:theory and applications[J].Acta Applicandae Mathematica,2001,66(3):211-249.
[5] KOVES M,MISANANTENAINA V R,WAGNER S.Steiner Wiener index and line graphs of trees[J].Discrete Mathematics Letters,2022,9:86-91.
[6] XU K X,LIU M H,DAS K,et al.A survey on graphs extremal with respect to distance-based topological indices[J].MATCH Commun Math Comput Chem,2014,71(3):461-508.
[7] GUTMAN I,LI S C,WEI W.Cacti with n vertices and t cycles having extremal Wiener index[J].Discrete Applied Mathematics,2017,232:189-200.
[8] LIU H Q,LU M.A unified approach to extremal cacti for different indices[J].Match Commun Math Comput Chem,2007,58(1):183-194.
[9] ZHANG J,ZHANG G J,WANG H,et al.Extremal trees with respect to the Steiner Wiener index[J].Discrete Mathematics,Algorithms and Applications,2019,11(6):1950067.
[10] LU L,HUANG Q X,HOU J X,et al.A sharp lower bound on Steiner Wiener index for trees with given diameter[J].Discrete Mathematics,2018,341(3):723-731.
[11] ZHANG J,WANG H,ZHANG X D.The Steiner Wiener index of trees with a given segment sequence[J].Applied Mathematics and Computation,2019,344/345:20-29.
[12] MAO Y P,WANG Z,GUTMAN I.Steiner Wiener index of graph products[J].Transactions on Combinatorics,2016,5(3):39-50.
[13] GUTMAN I,LI X L,MAO Y P.Inverse problem on the steiner Wiener index[J].Discussiones Mathematicae Graph Theory,2018,38(1):83-95.
[14] RASILA V A,VIJAYAKUMAR A.Bounds on the steiner-Wiener index of graphs[J].Discrete Mathematics,Algorithms and Applications,2022,14(6):2250017.
[15] ZHANG W P,MENG J X,WU B Y.The upper bounds on the steiner k-Wiener index in terms of minimum and maximum degrees[J].Journal of Combinatorial Optimization,2022,44(2):1199-1220.
[16] DANKELMANN P.The steiner k-Wiener index of graphs with given minimum degree[J].Discrete Applied Mathematics,2019,268:35-43.