What question did this study set out to answer?

The aim is to find trees with the highest non-self-centrality number within a specific class of trees.

April 16, 2026Open Access

Maximum Non-Self-Centrality Number of Trees With a Fixed Number of Pendant Vertices

Key Points

The aim is to find trees with the highest non-self-centrality number within a specific class of trees.
Defined the non-self-centrality number based on eccentricity of vertices.
Focused on n-vertex trees that have a specified number of pendant vertices.
Analyzed the characteristics of tree structures to determine maximum values.
Identified specific configurations of trees that maximize the non-self-centrality number.
Demonstrated a formula for calculating the non-self-centrality for trees with pendant vertices.
Contributed a solution to the problem posed by Farooq and Mudusar.

Abstract

The non-self-centrality number of an n-vertex, simple, and connected graph G is defined as N (G) = u =v |e(u) -e(v)|, where e(u) (respectively, e(v)) represents the eccentricity of the vertex u (respectively, v) in G, and the summation is taken over all unordered pairs of vertices of G. Let T(n, p) denote the class of n-vertex trees with p pendant vertices, where 4 p n -3.Farooq and Mudusar in Discrete Appl.Math.311 (2022) 26-34 proposed the problem of finding trees with the maximum non-self-centrality number in the class T(n, p).In this paper, we solve this problem.

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