The Steiner Wiener index of trees with a given segment sequence
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摘要
The Steiner distance of vertices in a set S is the minimum size of a connected subgraph that contain these vertices. The sum of the Steiner distances over all sets S of cardinality k is called the Steiner k-Wiener index and studied as the natural generalization of the famous Wiener index in chemical graph theory. In this paper we study the extremal structures, among trees with a given segment sequence, that maximize or minimize the Steiner k-Wiener index. The same extremal problems are also considered for trees with a given number of segments.
论文关键词:Steiner k-Wiener index,Segment sequence,Tree,Quasi-caterpillar
论文评审过程:Received 21 May 2018, Revised 28 September 2018, Accepted 1 October 2018, Available online 23 October 2018, Version of Record 23 October 2018.
论文官网地址:https://doi.org/10.1016/j.amc.2018.10.007