Corpus ID: 237571375

Partially ordering weighted trees using discrete Green's functions

  title={Partially ordering weighted trees using discrete Green's functions},
  author={Ji Zeng},
  • Ji Zeng
  • Published 19 September 2021
  • Mathematics
In this paper, we consider the edge transfer operation for which we remove an edge incident to a vertex and connect one of its neighbors to the other endpoint of this removed edge. We show that if an edge of a weighted tree is transferred from a vertex to another vertex with smaller diagonal value on the combinatorial Green’s function, the resulting tree has smaller Kemeny’s constant. Consequently, this leads to a partial order on the family of trees. Maximal and minimal elements of this… Expand

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