Partitioning of Wiener-type indices, especially for trees
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abstract
Different possible ways are noted to partition the so-called Wiener index of a molecular graph G into contributions associated to different substructures of G, particularly, for the case where G is a tree and the substructures are sites or bonds. Representative related partitionings for some related graph invariants are also established. Paralleling the definition of Wiener (or Hosoya) polynomials, the partitioning results are used to motivate Szeged polynomials.