University of KashanIranian Journal of Mathematical Chemistry2228-648914220230801Some Graph Operations and Titania Nanotubes in Reformulated Y-index and Reformulated S-index657611386510.22052/ijmc.2023.252551.1694ENKayalvizhiGokulathilaganDepartment of Mathematics, Kongu Arts and Science College, Erode, Tamil Nadu, India.0000-0003-4737-7377NagarajanSethumadhavanDepartment of Mathematics, Kongu Arts and Science College, Erode, Tamil Nadu, India.0000-0002-7747-9027Journal Article20230217Topological indices are numerical values that correlate a molecular graph’s physical and chemical properties. Titania nanotubes are a well-known semiconductor with a wide range of technological applications including biomedical devices, dye-sensitized solar cells, and so on. We offer two new graph invariants in this study known as the ‘Reformulated Y-index’ and ‘Reformulated S-index’. We calculate some special graphs and the Reformulated Y-index and S-index for some graph operations like as Join, Cartesian Product, Corona product, Corona join product, Subdivision vertex join and evaluate the Titania Nanotubes in Reformulated indices.https://ijmc.kashanu.ac.ir/article_113865_7a933a9af08161094752d6846f5f647a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914220230801Spectral Poly-Sinc Collocation Method for Solving a Singular Nonlinear BVP of Reaction-Diffusion with Michaelis-Menten Kinetics in a Catalyst/Biocatalyst779611373710.22052/ijmc.2023.246752.1648ENAliEftekhariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran0000-0001-5795-6634Journal Article20220813In this paper we revisit a nonlinear singular boundary value problem (SBVP) which arises frequently in mathematical model of diffusion and reaction in porous catalysts or biocatalyst pellets. A new simple variant of sinc methods so-called poly-sinc collocation method, is presented to solve non-isothermal reaction-diffusion model equation in a spherical catalyst and reaction-diffusion model equation in an electroactive polymer film. This method reduces each problem into a system of nonlinear algebraic equations, and on solving them by Newton's iteration method, we obtain the approximate solution. Through testing with numerical examples, it is found that our technique has exponentially decaying error property and performs well near singularity like other conventional sinc methods. The obtained results are in good agreement with previously reported results in the literature, and there is an impressive degree of agreement between our results and those obtained by a MAPLE ODE solver. Furthermore, the high accuracy of method is verified by using a residual evaluation strategy.https://ijmc.kashanu.ac.ir/article_113737_6723390009683f3afbfb3bb99a5ec814.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914220230801On a Conjecture on Edge Mostar Index of Bicyclic Graphs9710811386610.22052/ijmc.2023.248632.1680ENLijuAlexDepartment of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001
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Department of Mathematics, Marthoma College, Pathanamthitta - 689103, India0000-0003-2263-1324IndulalGopalapillaiDepartment of Mathematics, St. Aloysius College, Edathua, Alappuzha - 689573, India0000-0002-6673-9751Journal Article20221202For an edge e = uv of a graph G, mu(e|G) denotes the number of edges closer<br />to the vertex u than to v (similarly mv(e|G)). The edge Mostar index Moe(G), of a graph<br />G is defined as the sum of absolute differences between mu(e|G) and mv(e|G) over all<br />edges e = uv of G. H. Liu et al. proposed a Conjecture on extremal bicyclic graphs with<br />respect to the edge Mostar index [1]. Even though the Conjecture was true in case of the<br />lower bound and proved in [2], it was wrong for the upper bound. In this paper, we<br />disprove the Conjecture proposed by H. Liu et al. [1], propose its correct version and<br />prove it. We also give an alternate proof for the lower bound of the edge Mostar index<br />for bicyclic graphs with a given number of vertices.https://ijmc.kashanu.ac.ir/article_113866_a4ed9d93b3ca02a832e1d847446b73c7.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914220230801Acyclic Coloring of Certain Chemical Structures10912011386710.22052/ijmc.2023.248463.1670ENV. VinithaNavisSchool of Advanced Sciences, Vellore Institute of Technology, Chennai – 600127, IndiaA. BerinGreeniSchool of Advanced Sciences, Vellore Institute of Technology, Chennai – 600127, India0000-0002-3722-3342Journal Article20221019A rapidly developing field of science and technology is nanobiotechnology. Nanotube, nanostar and polyomino chain are critical and widespread molecular structures extensively used in the domains of pharmaceuticals, chemical engineering, and medical science. Additionally, these structures serve as the foundational building blocks for other, more intricate chemical molecular structures. In this paper, certain chemical structures like nanostar dendrimer, oxide network, silicate network, boron nanosheet and polyomino chains have been acyclically colored using the concept of vertex cut and matching. Also, we determine the acyclic coloring parameters for the networks under consideration and find a relation between them.https://ijmc.kashanu.ac.ir/article_113867_ec6036d486e77a428a39c32b98e0d575.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914220230801General Randi´c Index of uniform Hypergraphs12113311386810.22052/ijmc.2023.252836.1712ENGholam HassanShirdelDepartment of Mathematics, University of Qom, Qom, I. R. Iran0000-0003-2759-4606AmenehMortezaeeDepartment of Mathematics, University of Qom, Qom, I. R. Iran0000000171276651LaithAlameriDepartment of Mathematics, University of Qom, Qom, I. R. Iran0009-0007-1115-1719Journal Article20230420The general Randi´c index of a graph G = (V,E) was defined as<br />R_α=∑_(u,v∈V)(d_u d_v )^α , where du is the degree of vertex u and α is<br />an arbitrary real number. In this paper we define the Randi´c index<br />of a uniform hypergraph and obtain lower and upper bounds for Rα<br />depending different values of α.https://ijmc.kashanu.ac.ir/article_113868_d22418012a7ce9d5df67eb59de5f9539.pdf