More on inverse degree and topological indices of graphs

Suresh Elumalai, Sunilkumar M. Hosamani, Toufik Mansour, Mohammad Ali Rostami

Research output: Contribution to journalArticlepeer-review


The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of 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 (Randić 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 Randić index chemical trees in [16].

Original languageEnglish
Pages (from-to)165-178
Number of pages14
Issue number1
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2018, University of Nis. All rights reserved.


  • First Zagreb index
  • Inverse degree
  • Second Zagreb index

ASJC Scopus subject areas

  • General Mathematics


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