Extremal benzenoid systems for two modified versions of the Randić index

Fengwei Li, Hajo Broersma, Juan Rada and Yuefang Sun

Applied Mathematics and Computation, 2018, vol. 337, issue C, 14-24

Abstract: 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)−12, where du denotes the degree of u ∈ V. Bollobás and Erdős (1998) generalized this index by replacing −12 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{duα,dvα} and Rα″(G)=∑uv∈Emax{duα,dvα}. 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.

Keywords: Randić index; Generalized Randić index; Inlet; Benzenoid system; Catacondensed benzenoid system (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318304247
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:14-24

DOI: 10.1016/j.amc.2018.05.021

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().