University of KashanIranian Journal of Mathematical Chemistry2228-648913220220601Chemical Hyperstructures for Elements with Four Oxidation States859711203710.22052/ijmc.2022.246174.1615ENMadeleineAl-TahanDepartment of Mathematics and Statistics, Abu Dhabi University, United Arab Emirates0000-0002-4243-7935BijanDavvazDepartment of Mathematical Sciences, Yazd University, IranJournal Article20220313Algebraic hyperstructures represent a natural extension of classical algebraic structures and they have many applications in various sciences. In this paper, we investigate mathematical structures of chemical reactions for arbitrary elements with four oxidation states.https://ijmc.kashanu.ac.ir/article_112037_8548c052e1d08672aacfb2de630fd9ca.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913220220601Another Approach to a Conjecture about the Exponential Reduced Sombor Index of Molecular Trees9910811203110.22052/ijmc.2022.246488.1632ENAliGhalavandDepartment of Applied Mathematics, Faculty of Mathematical Sciences Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, Iran0000-0002-8186-0146MostafaTavakoliDepartment of Applied Mathematics, Faculty of Mathematical Sciences Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, IranJournal Article20220612For a graph <em>G</em>, the exponential reduced Sombor index (ERSI), denoted by e<sup>So<sub>red</sub></sup> , is ∑<sub>uv∈E(G)</sub> <span style="font-size: 11.1111px;">e</span><sup>√(d<em><sub>G</sub></em>(<em>v</em>)-1)^2+(d<em><sub>G</sub></em>(<em>u</em>)-1)^2),</sup> where d<em><sub>G</sub></em>(<em>v</em>) is the degree of vertex <em>v</em>. The authors in [On the reduced Sombor index and its applications, MATCH Commun. Math. Comput. Chem. 86 (2021) 729–753] conjectured that for each molecular tree <em>T</em> of order <em>n</em>, e<sup>So<sub>red</sub></sup>(<em>T</em>)≤(2/3) (<em>n</em>+1) e<sup>3</sup> +(1/3) (<em>n</em>-5) e <sup>3√2</sup>, where <em>n</em>≡2 (mod 3), e<sup>So<sub>red</sub></sup>(<em>T</em>)≤(1/3) (2<em>n</em>+1) e<sup>3</sup> +(1/3) (<em>n</em>-13) e<sup>3√2 </sup>+ 3e<sup>√13 </sup>, where <em>n</em>≡1 (mod 3) and e<sup>So<sub>red</sub></sup>(<em>T</em>)≤(2/3) <em>n</em>e<sup>3</sup> +(1/3) (<em>n</em>-9) e<sup>3√2 </sup>+ 2e<sup>√10 </sup>, where <em>n</em>≡0 (mod 3). Recently, Hamza and Ali [On a conjecture regarding the exponential reduced Sombor index of chemical trees. Discrete Math. Lett. 9 (2022) 107–110] proved the modified version of this conjecture. In this paper, we adopt another method to prove it. https://ijmc.kashanu.ac.ir/article_112031_9a77b0a18799e9ef991fd52ef5f9359d.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913220220601On the Minimal Unicyclic and Bicyclic Graphs with Respect to the Neighborhood First Zagreb Index10912811204710.22052/ijmc.2022.242939.1571ENShamailaYousafDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanCES, Lahore, PakistanDepartment of Mathematics, University of Gujrat, Gujrat, Pakistan0000-0003-2732-6601Akhlaq AhmadBhattiDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanJournal Article20210704The neighborhood ﬁrst Zagreb index has recently been introduced for characterizing the topological structure of molecular graphs. In the present study, we characterize the graphs having minimum neighborhood ﬁrst Zagreb index in the class of unicyclic/bicyclic graphs on vertices for every ﬁxed integer n ≥ 5.https://ijmc.kashanu.ac.ir/article_112047_94fedec74dc56fdbe9d02a52f617cb69.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913220220601Investigation of Closed Derivation Formulas for GQ and QG Indices of a Graph via M-polynomial12914411204810.22052/ijmc.2022.246172.1614ENShibsankarDasDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India0000-0003-0082-6673VirendraKumarDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India0000-0003-0393-4979Journal Article20220312A topological index is a numerical data which significantly correlates with the fundamental topology of a given chemical structure. The M-polynomial is a key mathematical tool to determine the degree-dependent topological indices. Very recently, the geometric-quadratic (GQ) and quadratic-geometric (QG) indices of a graph are introduced and computed their values by their respective mathematical formulas on some standard graphs and jagged-rectangle benzenoid system. In this research work, we propose M-polynomial based closed derivation formulas for determining the above two indices. In addition, we derive the GQ and QG indices for each of the abovementioned graphs by applying the derivation formulas, and also produce some fundamental relationships between the indices.https://ijmc.kashanu.ac.ir/article_112048_486722c0aa89c40cb10d0766135e86e9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913220220601Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching14516511205210.22052/ijmc.2022.243396.1605ENAbhayRajpootDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, INDIA0000-0003-3301-8285LavanyaSelvaganeshDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, INDIA0000-0002-8208-5372Journal Article20220105In this article, we complement the study of Pan and Li by computing the first five minimum values of the symmetric division degree (<em>SDD</em>) index attained by bicyclic graphs that have a perfect matching. One of our main contributions is identifying the graphs that attain the bounds. Further, we compute the upper bound of the <em>SDD</em> index for bicyclic graphs with a maximum degree of four, which admits a perfect matching and prove the bound is also tight by identifying the graphs that attain it.https://ijmc.kashanu.ac.ir/article_112052_cba8cca77a941af620e8337dd759b593.pdf