Research Article
On Analysis of Banhatti Indices for Hyaluronic Acid Curcumin
and Hydroxychloroquine
Wenhu Wang,
1,2
Muhammad Naeem ,
3
Abdul Rauf ,
3
Ayesha Riasat,
4
Adnan Aslam ,
5
and Kraidi Anoh Yannick
6
1
School of Software, Pingdingshan University, Pingdingshan 467000, China
2
College of Computing and Information Technologies, National University, Manila PH1008, Philippines
3
Department of Mathematics, Air University Multan Campus, Multan, Pakistan
4
Department of Basic Sciences and Humanities, University of Engineering and Technology, New Campus, Lahore, Pakistan
5
Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore(RCET), Pakistan
6
UFR of Mathematics and Computer Science, University Felix Houphouet Boigny of Cocody, Abidjan, Cˆ ote d’Ivoire
CorrespondenceshouldbeaddressedtoKraidiAnohYannick;kayanoh2000@yahoo.fr
Received 6 November 2021; Revised 10 December 2021; Accepted 11 December 2021; Published 31 December 2021
AcademicEditor:HaidarAli
Copyright©2021WenhuWangetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Topological indices are numerical numbers assigned to the graph/structure and are useful to predict certain physical/chemical
properties.Inthispaper,wegiveexplicitexpressionsofnovelBanhattiindices,namely,firstKBanhattiindex (B
1
(G)),secondK
Banhatti index (B
2
(G)), first K hyper-Banhatti index (HB
1
(G)), second K hyper-Banhatti index (HB
2
(G)), and K Banhatti
harmonic index (H
b
(G)) forhyaluronicacidcurcuminandhydroxychloroquine.emultiplicativeversionoftheseindicesis
also computed for these structures.
1. Introduction
Achemicalgraphmayberepresentedmathematicallyinthe
form of a polynomial, a numerical value, or a matrix. e
vertexofachemicalgraphsymbolizestheatoms,whilethe
edgesindicatethebondsbetweentheatomsinthemolecule
being studied. Over the years, mathematicians and others
involved in mathematical chemistry have calculated and
utilized many kinds of numerical numbers associated with
chemicalgraphstoanalyzeandresearchtheircharacteristics.
Chemical reaction network theory is concerned with
modelling the behaviour of real-world chemical systems. It
has been a hot cake for the research community from its
inception,owingtoitsimportanceintwosignificantfields,
namely, biochemistry and theoretical chemistry. It also has
a prominent position in pure mathematics, owing to its
mathematical structures.
Topological indices are numerical numbers assigned
toamoleculargraph.eyareveryhelpfulinthestudyof
physical, chemical, and structural characteristics of
chemical graphs, including boiling point, molecular
weight,density,andtoxicity.eWienerindexwasoneof
thefirstofitskind,presentedbyWiener[1].Heobserved
a relation between the boiling point of paraffin and the
Wiener index. e Randic index, Zagreb index, and the
Szeged index [2–4] are some of the most well-known
topological indices used to investigate the quantitative
structure-activity (QSAR) and quantitative structure-
property (QSPR) relationships of chemical graphs and
nanostructures [5–10].
Let G beasimpleconnectedgraphwithitsedgesetand
vertexsetdenotedby E and V,respectively.eorderof G is
the cardinality of set V. Similarly, the size of G is the car-
dinality of set E. Let u ∈ V and the set N(u)� v ∈ {
V | uv ∈ E} contains all the neighbors of u. We denote the
degreeofavertex u by d
u
andisthenumberofelementsin
N(u).edegreeofanedge e � uv isdenotedby d
e
andis
defined as d
e
� d
u
+ d
v
− 2. We use the notation ue if the
vertex u isincidenttoanedge e.Forbasicconceptsrelatedto
graphtheory,wereferthereaderstothebookbyWest[11].
Hindawi
Journal of Chemistry
Volume 2021, Article ID 7468857, 10 pages
https://doi.org/10.1155/2021/7468857