https://ijmc.kashanu.ac.ir/ Iranian Journal of Mathematical Chemistry en daily 1 Mon, 01 Jun 2026 00:00:00 +0330 Mon, 01 Jun 2026 00:00:00 +0330 https://ijmc.kashanu.ac.ir/article_115558.html ‎The 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_115563.html ‎The 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:‎ Let G be a simple connected graph on $n$ vertices‎. ‎Then‎ Mo(L_G)<= Mo(G).‎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_115564.html ‎In 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_115589.html ‎It 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_115590.html ‎The 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_115593.html ‎A 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.