The Steiner $k$-eccentricity on trees
Combinatorics
2020-08-19 v1
Abstract
We study the Steiner -eccentricity on trees, which generalizes the previous one in the paper [X.~Li, G.~Yu, S.~Klav\v{z}ar, On the average Steiner 3-eccentricity of trees, arXiv:2005.10319, 2020]. To support the algorithm, we achieve much stronger properties for the Steiner -ecc tree than that in the previous paper. Based on this, a linear time algorithm is devised to calculate the Steiner -eccentricity of a vertex in a tree. On the other hand, the lower and upper bounds of the average Steiner -eccentricity index of a tree on order are established based on a novel technique which is quite different from that in the previous paper but much easier to follow.
Keywords
Cite
@article{arxiv.2008.07763,
title = {The Steiner $k$-eccentricity on trees},
author = {Xingfu Li and Guihai Yu and Sandi Klavžar and Jie Hu and Bo Li},
journal= {arXiv preprint arXiv:2008.07763},
year = {2020}
}