Extremal benzenoid systems for two modified versions of the Randić index

Fengwei Li, Hajo Broersma*, Juan Rada, Yuefang Sun

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


Let G=(V,E) be a molecular graph, in which the vertices of V represent atoms and the edges of E the bonds between pairs of atoms. One of the earliest and most widely studied degree-based molecular descriptor, the Randić index of G, is defined as R(G)=∑uv∈E(dudv)−[Formula presented], where du denotes the degree of u ∈ V. Bollobás and Erdős (1998) generalized this index by replacing −[Formula presented] with any fixed real number. To facilitate the enumeration of these indices, motivated by earlier work of Dvořák et al. (2011) and Knor et al. (2015) introduced two other indices, that provide lower and upper bounds, respectively: Rα (G)=∑uv∈Emin{du α,dv α} and Rα (G)=∑uv∈Emax{du α,dv α}. In this paper, we give expressions for computing Rα and Rα of benzenoid systems and phenylenes, as well as a relation between Rα and Rα of a phenylene and its corresponding hexagonal squeeze. We also determine the extremal values of Rα and Rα in benzenoid systems with h hexagons for different intervals for the value of α.

Original languageEnglish
Pages (from-to)14-24
Number of pages11
JournalApplied mathematics and computation
Publication statusPublished - 15 Nov 2018


  • Benzenoid system
  • Catacondensed benzenoid system
  • Generalized Randić index
  • Inlet
  • Randić index


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