Research Article Multiplicative Zagreb Indices of Molecular Graphs Xiujun Zhang , 1 H. M. Awais , 2 M. Javaid , 2 and Muhammad Kamran Siddiqui 3 1 School of Information Science and Engineering, Chengdu University, Chengdu 610106, China 2 Department of Mathematics, School of Science, University of Management and Technology (UMT), Lahore 54770, Pakistan 3 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan Correspondence should be addressed to M. Javaid; javaidmath@gmail.com Received 1 November 2019; Accepted 19 November 2019; Published 6 December 2019 AcademicEditor:JuanL.G.Guirao Copyright©2019XiujunZhangetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mathematicalmodelingwiththehelpofnumericalcodingofgraphshasbeenusedinthedifferentfieldsofscience,especiallyin chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as (Γ)�  p∈V(Γ) [d Γ (p) 2 ] and  1 (Γ)�  pq∈E(Γ) [d Γ (p)+ d Γ (q)],respectively.InthesamepaperofTodeshine,theyalsodefinedthe2ndmultiplicativeZagreb indexas  2 (Γ)�  pq∈E(Γ) [d Γ (p)× d Γ (q)]. Recently,Liuetal.[IEEEAccess;7(2019);105479–-105488]definedthegeneralized subdivision-relatedoperationsofgraphsandobtainedthegeneralizedF-sumgraphsusingtheseoperations.eyalsocomputed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included. 1. Introduction enumericaldemonstrationofamoleculargraphcanbe assumed as a single number, commonly known as to- pological index (TI). ere are many interesting and significant results about TIs to study the different properties of chemical compounds such as chromato- graphic retention times, heat of formation and evapo- ration,flashpoint,viscosity,freezing,boilingandmelting point, octanol-water partition coefficient, surface ten- sion, stability, temperature, density, weight, polariz- ability, connectivity, and solubility. Many medicines, crystallineandnanomaterials,thatareusedinnumerous pharmaceutical industries are examined with the assis- tanceofdifferentTIs,see[1–7].TIsalsostudyQSPRand QSAR models that join molecular graphs to their mo- lecular characteristics by means of statistical tools. For additional information, see [8–17]. In 1947, to investigate the paraffin’s boiling point, Wiener utilized the distance-based TI [18]. Gutman and Trinajsti´ c [19] determined a pair of degree-based first and second Zagreb indices. After this, different impressive TIs are introduced in molecular graph theory [20,21], but the degree-based TIs are famous than others, see [22]. Ingraphtheory,thevariousoperationsondifferentgraphs showanimportantroleinthecreationofadvancedfamiliesof graphs, see [23,24]. Yan et al. [13] gave the idea of four op- erations S 1 ,R 1 ,Q 1 , and T 1 of graphs and computed the Wiener index of the resultant graphs obtained by using these operations.EliasiandTaeri[25]introducedthe F 1 -sumgraphs (Γ 1+F 1 Γ 2 ) byusingthecartesianproductofgraphs F 1 (Γ 1 ) and Γ 2 , where Γ 1 and Γ 2 are the two simple graphs and F 1 (Γ 1 ) is obtained by using F 1 ∈ S 1 ,R 1 ,Q 1 , & T 1  . ey also de- termined the Wiener index of these F 1 -sum graphs. Addi- tionally,Dengetal.[26],ImranandAkhtar[27],Shirdeletal. [28], and Liu et al. [29] determined the 1st and 2nd Zagreb Hindawi Journal of Chemistry Volume 2019, Article ID 5294198, 19 pages https://doi.org/10.1155/2019/5294198