On the average Steiner 3-eccentricity of trees

TL;DR

This paper investigates the Steiner 3-eccentricity in trees, providing properties, a transformation that preserves or reduces it, and establishing bounds for its average value.

Contribution

It introduces a tree transformation that does not increase the average Steiner 3-eccentricity and derives bounds for this measure in trees.

Findings

A tree transformation that does not increase average Steiner 3-eccentricity

General properties of Steiner 3-eccentricity in trees

Lower and upper bounds for the average Steiner 3-eccentricity

Abstract

The Steiner $k$-eccentricity of a vertex $v$ of a graph $G$ is the maximum Steiner distance over all $k$-subsets of $V(G)$ which contain $v$. In this paper Steiner $3$-eccentricity is studied on trees. Some general properties of the Steiner $3$-eccentricity of trees are given. A tree transformation which does not increase the average Steiner $3$-eccentricity is given. As its application, several lower and upper bounds for the average Steiner $3$-eccentricity of trees are derived.