The Steiner k-eccentricity on trees

Abstract We study the Steiner k-eccentricity on trees, which generalizes the previous one in the paper [On the average Steiner 3-eccentricity of trees, arXiv:2005.10319 ]. We achieve much stronger properties for the Steiner k-ecc tree than that in the previous paper. Based on this, a linear time algorithm is devised to calculate the Steiner k-eccentricity of a vertex in a tree. On the other hand, lower and upper bounds of the average Steiner k-eccentricity index of a tree on order n are established based on a novel technique which is quite different and also much easier to follow than the earlier one.