University of KashanIranian Journal of Mathematical Chemistry2228-648917220260601New Results on Second Inverse Sum Indeg Index11312811555810.22052/ijmc.2025.257454.2055ENDariushHeidariFaculty of science, Mahallat Institute of Higher Education, Mahallat, IranMohamadrezaRostamiFaculty of science, Mahallat Institute of Higher Education, Mahallat, IranIvanGutmanFaculty of Science, University of Kragujevac, Kragujevac, SerbiaLijuAlexBishop Chulaparambil Memorial College, Kottayam-686001, IndiaJournal Article20250819The second inverse sum indeg topological index $(ISI_2)$ is considered as a valuable tool for the study of graphs and trees. This index is systematically investigated for the first time, and its upper and lower bounds are derived for general graphs and trees. Furthermore, comparisons between $ISI_2$ and other existing topological indices are presented. The results demonstrate that $ISI_2$ not only provides valuable insights into the structure of graphs but also serves as a powerful instrument for modeling and analyzing complex networks, particularly in chemistry and pharmacology. Specifically, $ISI_2$ exhibits significant potential in predicting physicochemical properties of molecules, such as polarity, boiling point, and biological activity. Thus, $ISI_2$ may serve for the design and optimization of novel drug molecules and chemical compounds.https://ijmc.kashanu.ac.ir/article_115558_f4ae081b9d19512aad6a751a44c19dff.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917220260601Counterexamples to a Conjecture on the Mostar Index of a Graph and its Line Graph12913611556310.22052/ijmc.2026.257415.2052ENLijuAlexDepartment of Applied Science, Rajiv Gandhi Institute of Technology, Kottayam-686501, IndiaGopalapillaiIndulalDepartment of Mathematics, St.Aloysius College, Edathua, Alappuzha -689573, IndiaJournal Article20250813The Mostar index is a distance-based topological index defined as a quantitative measure of distance balancedness and peripherality in graphs. Recently, in “An inequality for the Mostar index of line graphs of trees” [Commun. Comb. Optim. (2005), doi: 10.22049/cco.2025.30201.2356], the following conjecture regarding the Mostar index of graphs and their line graphs was proposed:<br /> Let G be a simple connected graph on $n$ vertices. Then Mo(L_G)<= Mo(G).<br />where, L_G denotes the line graph of the graph G. In this paper, counterexamples are presented to disprove the conjecture proposed in \cite{sardar2025inequality}. We also prove that the conjecture is not true for an infinite family of graphs with fixed cyclomatic number $c$, where $1 \le c\le 3$.https://ijmc.kashanu.ac.ir/article_115563_2ff05a505767a9423b073bf4d67a7119.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917220260601Extended Fractional-Time Oregonator Model Accounting for Proton Dynamics13717711556410.22052/ijmc.2025.257706.2074ENSaritaPippalDepartment of Mathematics, Panjab University, Chandigarh, IndiaJournal Article20251004In this manuscript, we develop a generalized form of the classical three-variable Oregonator model by extending it to a four--dimensional fractional-order system. The extended formulation explicitly includes the proton concentration $\mathcal{H}(t)$ within the Belousov-Zhabotinsky (BZ) reaction kinetics and introduces memory effects through the Caputo fractional derivative of order $\alpha\in(0,1]$. For the classical case $\alpha = 1$, the model reduces to an ordinary differential equation system, which is solved using the third-order Adams-Bashforth-Moulton (ABM3) predictor-corrector method and compared with the standard fourth-order Runge-Kutta (RK4) scheme. For $0 <\alpha<1$, the system is numerically integrated using the fractional ABM3 method, where the Caputo derivative is discretized by means of convolution-type memory weights. Numerical experiments reveal that both proton feedback plays a crucial role in shaping the oscillatory dynamics and stabilizing the long-term behavior. Analytical results further confirm positivity and boundedness of the solutions, characterize the equilibrium points, and determine their stability. The trivial equilibrium is always unstable, whereas the nontrivial equilibrium is locally asymptotically stable under realistic parameter conditions. Sensitivity and eigenvalue analysis additionally show that the parameters (a, q) tend to destabilize the system, while $(\delta, \varepsilon, \gamma)$ enhance stability. Here, a and q represent the autocatalytic and inhibition reaction strengths, whereas $\delta$, $\varepsilon$, and $\gamma$ denote the characteristic timescales of the inhibitor, autocatalyst, and proton dynamics, respectively.https://ijmc.kashanu.ac.ir/article_115564_97c1e0da98ad28ed90d7d713eeaf02c2.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917220260601Matching Polynomials and Independence Polynomials of Hexacyclic Systems17919911558910.22052/ijmc.2025.257868.2080ENHanlinChenSchool of Mathematics, Changsha University, Changsha 410022, P. R. China0000-0003-3692-5411Journal Article20251029It is well established that matching and independence polynomials hold great significance in mathematical chemistry, serving as core tools to bridge the topological features of molecular graphs with quantifiable chemical properties.Against this backdrop, this paper focuses on computing the matching and independence polynomials of both hexacyclic systems and their Möbius counterparts. Building upon the research presented in"Matching polynomials and independence polynomials of benzenoid chains" [\textit{MATCH Commun. Math. Comput. Chem.} \textbf{92} (2024) 779-809], we first develop methods to determine the matching and independence polynomials for an arbitrary hexacyclic system $F_{\vartheta_1\vartheta_2\cdots\vartheta_{h}}$ and its Möbius counterpart $M_{\vartheta_1\vartheta_2..\vartheta_{h}}$. Subsequently, computational formulas for the Hosoya index and Merrifield-Simmons index of both systems are derived.https://ijmc.kashanu.ac.ir/article_115589_b336692a123fed719c50bcb0185eab89.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917220260601Topological Indices and Disjoint Path Cover Property of Graphs20121611559010.22052/ijmc.2026.257594.2067ENHonggangZhaoCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. ChinaEminjanSabirCollege of Mathematics and System Sciences, Xinjiang University, Urumqi,
830046, P. R. ChinaJournal Article20250916The disjoint path cover problem is closely related to the well-known Hamiltonian problem, which is a fundamental concept in graph theory. In the domains of bioinformatics and neuroinformatics, the existence of a disjoint path cover indicates the cascade effect within the signal transduction system and the reaction occurring in a metabolic pathway. One of the core subjects in exploring the disjoint path cover problem is to develop sufficient conditions. In this paper, we provide novel sufficient conditions, with respect to some significant topological indices including Harary index, first Zagreb index, forgotten topological index, reciprocal degree distance, eccentric connectivity index, eccentric distance sum, and connective eccentric index, for a connected graph to be disjoint path coverable.https://ijmc.kashanu.ac.ir/article_115590_603a045d62fb25e25661a3920393205c.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648917220260601An Appropriate Fractional Narayana Polynomials Neural Network Method for a Mathematical Model of the Lung Cancer21723211559310.22052/ijmc.2026.258001.2093ENHosseinHassaniDepartment of Mathematics, Anand International College of Engineering, Jaipur 303012, IndiaZakiehAvazzadehStony Brook Institute at Anhui University, Anhui University, Hefei 230601, ChinaArzuTuran-DincelDepartment of Mathematical Engineering, Yildiz Technical University, 34220, Esenler, Istanbul-TurkeyAliBayati EshkaftakiFaculty of Mathematics, Shahrekord University, Shahrekord, IranLeilaZahiriDepartment of Internal Medicine, Shiraz University of Medical Sciences, Shiraz, IranJournal Article20251121A mathematical model of lung cancer is used to analyze the dynamics of tumor growth and the interactions between cancer cells and immune cells. To obtain approximate solutions and improve understanding of the behavior of the state functions, a fractional Narayana polynomials neural network (FNPNN) with higher accuracy and better efficiency is proposed. For this purpose, we develop a method using a three-layer artificial neural network, which includes an input layer, a hidden layer, and an output layer. The fractional Narayana polynomials and $arcsinh(t)$ function are utilized as activation functions for the hidden and output layers of the network, respectively. The lung cancer model is reduced to the problem of solving a system of algebraic equations through the use of FNPNN and the Lagrange multipliers method. All computations are performed using Maple and MATLAB software. The convergence analysis is discussed. The efficiency and versatility of our suggested approach are confirmed by numerical modeling examples. The technique proposed in this work can be effortlessly applied to other scientific or engineering problems, providing the potential for substantial efficiency gains while keeping accuracy at an acceptable level.https://ijmc.kashanu.ac.ir/article_115593_830000ec32bfd37942d999b801e84d62.pdf