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

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.