The eccentric harmonic index of trees

Abstract

Topological indices play an important role in mathematical chemistry, particularly in studies of quantitative structure property and quantitative structure activity relationships. The eccentric harmonic index of G is defined as where uv is an edge of G, e(u) is the eccentricity of the vertex u in G. In this paper, we will determine the maximum and minmum eccentric harmonic index of trees in terms of graph parameters such as pendant number and matching number, and characterize corresponding extremal graphs.