Some Bounds for Topological Efficiency of Graphs

Abstract

In this paper we present explicit formulas for computing the topological efficiency index under some important graph operations such as disjunction, symmetric difference and rooted product of two graphs. Abo, we apply our results to compute this distance-related invariant for some important classes of molecular graphs such as caterpillars and chain graphs by specializing components of rooted product. In the sequel, we obtain some bounds for the topological ef-ficiency index of a graph in terms of Wiener index, total eccentricity and some other graphical parameters such as the number of vertices, number of edges, radius and the diameter of a graph. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.