Maximum Wiener Index of Trees with Given Degree Sequence

By Xiaodong Zhang, Y. Liu, Min-Xian Han. 2010

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Greedy Trees, Caterpillars, and Wiener-Type Graph Invariants (2012, background): “[27] first pointed out the complexity of the question and studied cases for trees with few internal vertices.”
Survey on Geometric-Arithmetic Indices of Graphs (2011, methodology): “Hence, the probably best known and most widely used Wiener index [12,90,93] is based on topological distance of vertices in the respective graph, the Hosoya index [53,66] is calculated by counting non-incident edges in a graph, the energy [31, 35, 46] and the Estrada index [23, 94] are based on the ”