Research Article Structural Analysis and Topological Characterization of Sudoku Nanosheet Shahid Zaman , 1 Mehwish Jalani, 1 AsadUllah , 2 and Ghulamullah Saeedi 3 1 Department of Mathematics, University of Sialkot, Sialkot 51310, Pakistan 2 Department of Mathematical Sciences, Karakoram International University Gilgit, Gilgit•Baltistan 15100, Pakistan 3 Department of Mathematics, Polytechnical University of Kabul, Kabul, Afghanistan Correspondence should be addressed to Ghulamullah Saeedi; gh.saeedi@kpu.edu.af Received 24 September 2022; Revised 24 October 2022; Accepted 31 October 2022; Published 16 November 2022 Academic Editor: Elena Guardo Copyright©2022ShahidZamanetal.TisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tephysicalandbiologicalpropertiesofchemicalcompoundsaremodelledusingchemicalgraphtheory.Tegeometricstructure ofchemicalcompoundscanbemodelledusingavarietyoftopologicalindicesderivedfromgraphtheory.Techemicalstructures, physicochemical characteristics, and biological activities are predicted by the topological indices using the real numbers derived from the molecular compound. Te topological index’s frst use was to identify the physical characteristics of alkenes. A to• pological index is a molecular structure descriptor calculated from a chemical compound’s molecular graph describing its topology.Whenappliedtoachemicalcompound’smolecularstructure,ittellsthetheoreticalproperties.Techemicalstructureis studiedasagraph,whereelementsaredenotedasvertices,andchemicalbondsarecallededges.Inthisstudy,wehavecomputed somenoveltopologicalindicesnamedasmodifedneighborhoodversionoftheforgottentopologicalindex F ∗ N ,theneighborhood version of the frst multiplicative Zagreb M ∗ 1 , the neighborhood version of the second Zagreb index M ∗ 2 , the neighborhood versionofhyper•ZagrebindexHM N ,theSambortopologicalindexSO(G),andtheSamborreducedtopologicalindexSO red (G) fortheSudokunanosheetandderivedformulasforthem.Basedonthederivedformulas,thenumericalresultsoftheunderstudy nanosheet’s physical and chemical properties are investigated. Our computed results are undoubtedly helpful in understanding the topology of the understudy nanosheet. Tese computed indices have the best correlation with acentric factor and entropy; therefore, they are efective in QSPRs and QSARs analysis with complete accuracy. 1.Introduction Te subject of intense research is the famous 2•dimensional nano•material graphene, the world’s [1–3] lightest 2D ma• terial with a hexagonal grid. Since their inventions, carbon nanotubes have gained a lot of attention [4, 5]. Carbon nanotubes (CNTs) are made of carbon using nanometer diameters. Te one•wall carbon nanotubes are a bore in the variety of nanometers by Iijima and Ichihashi [4], and Bethune et al. [5] independently. Te thickness of the 2D nanostructure varies from 1 to 100nm [6]. Tese 2D nanosheets have interesting physical, electronic, biological, and chemical properties that are essential for various ap• plications. Terefore, it is critical to predicting these nanostructures to attain discrimination and bring about the network topology, meliorate, and their physical character• istics.Chemicalgraphtheoryisusedtorepresentbetterand characterise molecules to understand chemical compounds’ physical properties [7]. Graphs are mathematical structures that are used to model relationships. A Chemical graph is a basic calculable graph with atoms at the edge in an implicit system.In[8],Randic'givestheconceptof fndingasuitable path to reach the desire vertex. A TI describes a lot of prominent properties of some chemical compounds. Tese are essential in biological and chemical science and engineering. Physicochemical character• istics or theoretical molecular descriptors are used as forecasters in QSAR modelling [9–11], whilst the expression QSPR models as replication variables [12–15]. Wiener [16] introduced the TI conceptwhilefunctioningonparafn’sboilingpointandsetitas Hindawi Journal of Mathematics Volume 2022, Article ID 5915740, 10 pages https://doi.org/10.1155/2022/5915740