Abstract
The terminal Wiener index of a tree is defined as the sum of distances between all leaf pairs of T. We derive closed form expression for the terminal Wiener index of fibonacci trees. We also describe a linear time algorithm to compute terminal Wiener index of a tree.
Highlights
For a tree T, the terminal Wiener index TW(T)[7] of T is defined as the sum of the distances between all pairs of leaves of T
Let Tfkb denote the binary Fibonacci tree of order k [2,10], is defined recursively in the following way: Tf0b and Tf1b are both rooted trees consisting of no nodes and a single node respectively
We propose a method to compute terminal Wiener index of fibonacci trees
Summary
For a tree T, the terminal Wiener index TW(T)[7] of T is defined as the sum of the distances between all pairs of leaves of T. Let T be an n-vertex tree with k leaves. The paper[9] describe a method to compute terminal Wiener index of balanced trees. Let Tfkb denote the binary Fibonacci tree of order k [2,10], is defined recursively in the following way: Tf0b and Tf1b are both rooted trees consisting of no nodes and a single node respectively. Its terminal Wiener index is given by TW(Tfk)=TW(Tfk-1)+TW(Tfk-2)+Fkd Tf +(k-2)+Fk-1 dTf+(k.
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