Some sharp bounds on the average Steiner (k, l)-eccentricity for trees

TL;DR

This paper introduces transformations for trees that do not increase the average Steiner (k,l)-eccentricity and uses them to establish sharp bounds for trees with specific properties, identifying extremal structures.

Contribution

It presents new transformations that preserve or reduce the average Steiner (k,l)-eccentricity and derives sharp bounds for trees with fixed parameters.

Findings

Established sharp bounds on average Steiner (k,l)-eccentricity for trees.

Identified extremal trees under various constraints.

Provided transformations that do not increase the eccentricity measure.

Abstract

In this paper we introduce some transformations for trees that do not increase the average Steiner $(k,l)$-eccentricity for all $0\leq l\leq k\leq n$. Using these transformations, we obtain some sharp bounds on the average Steiner $(k,l)$-eccentricity for trees with some certain conditions, including given nodes, given diameter, given max degree and given leaves, and get the corresponding extremal trees as well.