Comparison of novel index with geometric-arithmetic and sum-connectivity indices

Abstract

This work focusses on the minimal, second minimal, maximal and second maximal values of three indices for various unicyclic, bicyclic graphs. Motivated by the works of Ghorbani, this work compares the extremal values among three indices viz., geometric-arithmetic, sum-connectivity and proposed novel index (geometric-harmonic) and these indices are computed for star, cycle and path. Relations are established among the indices for star, cycle, path, tree, complete, unicyclic and bicyclic graphs.