On a general weight of trees
We define a general weight of the nodes of a given tree T; it depends on the structure of the subtrees of a node, on the number of interior and exterior nodes of these subtrees and on three weight functions defined on the degrees of the nodes appearing in T. Choosing particular weight functions, the weight of the root of the tree is equal to its internal path length, to its external path length, to its internal degree path length, to its external degree path length, to its number of nodes of some degree'r, etc.
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