A sharp lower bound on Steiner Wiener index for trees with given diameter |
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Authors: | Lu Lu Qiongxiang Huang Jiangxia Hou Xun Chen |
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Affiliation: | College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, PR China |
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Abstract: | Let be a connected graph with vertex set and edge set . For a subset of , the Steiner distance of is the minimum size of a connected subgraph whose vertex set contains . For an integer with , the Steiner-Wiener index is . In this paper, we introduce some transformations for trees that do not increase their Steiner -Wiener index for . Using these transformations, we get a sharp lower bound on Steiner -Wiener index for trees with given diameter, and obtain the corresponding extremal graph as well. |
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Keywords: | Distance Steiner distance Steiner Wiener index Caterpillar trees |
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