A series of novel substituted benzaldehyde derivatives of 4-Amino-7H-pyrrolo[2,3-d]pyrimidine (4A7HPP), designated as compounds 1a–1d, were synthesized under microwave irradiation, providing a safe, cost-effective, and efficient alternative to conventional procedures. The condensation of 4A7HPP with hydroxybenzaldehyde analogues in DMF afforded the corresponding imine derivatives in high yields (71.54–85.02%) with reduced reaction time and solvent consumption. The synthesized compounds were characterized by ¹H NMR, FT-IR, UV–Vis spectroscopy, and elemental analysis, confirming the presence of characteristic azomethine (–CH=N–) and aromatic proton signals. The compounds exhibited significant antibacterial activity against Staphylococcus aureus, Bacillus subtilis, Escherichia coli, and Pseudomonas aeruginosa (MIC: 7.5–28 mm), surpassing the standard drug streptomycin. Notably, antifungal evaluation against Candida albicans and Saccharomyces cerevisiae demonstrated activity up to 2.5 times greater than fluconazole. Molecular docking studies performed against target proteins—S. aureus DHFR (PDB ID: 2W9H), E. coli DHFR (PDB ID: 1RX2), and C. albicans ERG11 (PDB ID: 5TZ1)—revealed stronger binding affinities for compounds 1b and 1d (−8.3 to −9.0 kcal mol⁻¹) compared with reference ligands, supported by low RMSD values (0.655–0.785 Å). Brine shrimp lethality bioassay indicated moderate cytotoxicity (LD₅₀: 3.50–8.50 × 10⁻⁴ M). ADME analysis suggested favorable pharmacokinetic profiles, high gastrointestinal absorption, and compliance with Lipinski’s rule of five. These results highlight compounds 1a–1d as potential lead molecules for the development of new antimicrobial and antifungal agents, warranting further biological and pharmacological investigations.

Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to 3-dimensional geometry are given.Applications are suggested for priority assignment and optimization problems.

This paper initiates a study on a new optimization problem with regards to graph completion. A new iterative procedure called Marcello’s completion of a graph is defined. For graph \(G\) of order \(n\) the graphs, \(G_1,G_2,\dots,G_k\) are obtained in accordance to the Marcello rule. If for smallest \(k\) the resultant graph \(G_k \cong K_n\) then the Marcello number of a graph \(G\) denoted by \(\varpi(G)\) is equal to \(\varpi(G) = k\). By convention \(\varpi(K_n) = 0\), \(n \geq 1\). Certain introductory results are presented.

The atom-bond sum-connectivity \((ABS)\) matrix of a graph \(G\) is the square matrix of order \(n\), whose \((i,j)\)-entry is equal to \(\sqrt{1-\frac{2}{d_i+d_j}}\) if the \(i\)-th vertex and the \(j\)-th vertex of \(G\) are adjacent, and \(0\) otherwise, where \(d_i\) is the degree of the \(i\)-th vertex of \(G\). The \(ABS\) spectral radius of \(G\) is the largest eigenvalue of the \(ABS\) matrix of \(G\). Recently, we studied the extremal problem for the \(ABS\) spectral radii of trees and unicyclic graphs, determining which structures achieve the maximum and minimum values. In this paper, the unicyclic graphs and bicyclic graphs with the first two largest \(ABS\) spectral radii are characterized.

The increasing prevalence of electric vehicles (EVs) in urban logistics presents challenges such as route planning, energy constraints, and demand management. EVs’ limited range, charging requirements, and sensitivity to traffic conditions necessitate advanced optimization strategies. Fleet management systems are thus evolving into intelligent, modular platforms that not only plan delivery tasks but also interact with real-time data and respond to dynamic disruptions. Among these, traffic congestion remains a critical factor that can severely affect route reliability and lead to time window violations. In this study, a modular fleet management system architecture is proposed, capable of real-time monitoring, dynamic rerouting, and traffic-aware decision-making. The system introduces a standardized data structure called the Routing Markup Language (RML), which formalizes the communication between components and supports various route outputs including simulation and vehicle-level execution. Adaptive Large Neighborhood Search (ALNS) is applied for route planning using real-world order data from a water distribution company operating in the Büyükdere district of Eskişehir. The system also features a dynamic reassignment mechanism that responds to vehicle failure scenarios, ensuring continued operation with minimal disruption. Traffic scenarios are evaluated through the Simulation of Urban Mobility (SUMO) environment to assess route robustness under varying conditions. The proposed approach integrates routing optimization, dynamic disruption handling, and simulation-supported fleet monitoring into a cohesive system, offering a responsive and data-driven solution for sustainable urban logistics.