Operations Research Transactions ›› 2023, Vol. 27 ›› Issue (3): 178-184.doi: 10.15960/j.cnki.issn.1007-6093.2023.03.015

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Extremal problems for Steiner Wiener index of unicyclic graphs

Jie ZHANG1,*(), Yan JI2   

  1. 1. Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
    2. Pingyin Experimental School, Jinan 250400, Shandong, China
  • Received:2019-09-18 Online:2023-09-15 Published:2023-09-14
  • Contact: Jie ZHANG E-mail:zhangjie.sjtu@163.com

Abstract:

Wiener index is an important chemical index in chemical graph theory, defined as the sum of distances between all pairs of vertices. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of the Steiner distances over all sets S of cardinality k. The Steiner distance of vertices in a set S is the minimum size of a connected subgraph that contain these vertices. We consider the extremal problems with respect to the Steiner Wiener index among all unicyclic graphs.

Key words: Steiner Wiener index, Steiner distance, unicyclic graphs, Wiener index

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