Computing Wiener Index of Fibonacci Weighted Trees (original) (raw)

Given a simple connected undirected graph ‫ܩ‬ = ሺܸ, ‫ܧ‬ሻ with |ܸ| = ݊ and ‫|ܧ|‬ = ݉, the Wiener index ܹሺ‫ܩ‬ሻ of ‫ܩ‬ is defined as half the sum of the distances of the form ݀ሺ‫,ݑ‬ ‫ݒ‬ሻ between all pairs of vertices u, v of ‫ܩ‬. If ሺ‫,ܩ‬ ‫ݓ‬ ா ሻ is an edge-weighted graph, then the Wiener index ܹሺ‫,ܩ‬ ‫ݓ‬ ா ሻ of ሺ‫,ܩ‬ ‫ݓ‬ ா ሻ is defined as the usual Wiener index but the distances is now computed in ሺ‫,ܩ‬ ‫ݓ‬ ா ሻ. The paper proposes a new algorithm for computing the Wiener index of a Fibonacci weighted trees with Fibonacci branching in place of the available naive algorithm for the same. It is found that the time complexity of the algorithm is logarithmic.