The total Steiner k-distance for b-ary recursive trees and linear recursive trees
نویسنده
چکیده
We prove a limit theorem for the total Steiner k-distance of a random b-ary recursive tree with weighted edges. The total Steiner k-distance is the sum of all Steiner k-distances in a tree and it generalises the Wiener index. The limit theorem is obtained by using a limit theorem in the general setting of the contraction method. In order to use the contraction method we prove a recursion formula and determine the asymptotic expansion of the expectation using the so-called Master Theorem by Roura (2001).
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