Some Preliminary Result About the Inset Edge and Average Distance of Trees
Computational Complexity
2020-08-14 v1 Combinatorics
Abstract
An added edge to a graph is called an inset edge. Predicting k inset edges which minimize the average distance of a graph is known to be NP-Hard. However, when k = 1 the complexity of the problem is polynomial. In this paper, some tools for a precise analysis of the problem for the trees are established. Using the tools, we can avoid using the distance matrix. This leads to more efficient algorithms and a better analysis of the problem. Several applications of the tools as well as a tight bound for the change of average distance when an inset edge is added to a tree are presented.
Cite
@article{arxiv.2008.05677,
title = {Some Preliminary Result About the Inset Edge and Average Distance of Trees},
author = {M. H. Khalifeh and A. -H. Esfahanian},
journal= {arXiv preprint arXiv:2008.05677},
year = {2020}
}