Some Preliminary Result About the Inset Edge and Average Distance of Trees

M. H. Khalifeh; A. -H. Esfahanian

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arXiv · 2008.05677

Some Preliminary Result About the Inset Edge and Average Distance of Trees

M. H. Khalifeh·A. -H. Esfahanian

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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.

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M. H. Khalifeh, A. -H. Esfahanian. 2020-08-13. Some Preliminary Result About the Inset Edge and Average Distance of Trees. https://arxiv.org/abs/2008.05677

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