More On Inverse Degree and Topological Indices of Graphs

Suresh ELumalai, Sunilkumar M Hosamani, Toufik Mansour, Mohammed Ali Rostami


vertex degrees of the graph $G.$ In this paper, we obtain several lower and upper bounds on inverse degree $ID(G).$ Moreover, using  computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree $ID(G)$. Next, we compare inverse degree $ID(G)$ with topological indices (Randi{\'c} index $R(G)$, geometric-arithmetic index $GA(G)$)  for chemical trees and also we  determine the $n-$vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum  of $ID-R.$ In addition, we correct the second and third minimum Randi{\'c} index chemical trees in [16].

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