Saraswathi Narayanan College

This paper introduces strong fuzzy planar graphs (SFPLGs), extending fuzzy graph theory with a quantitative planarity measure theta(ohm) = 1/1+Sigma(n)(i=1) Lambda(theta(i)) that classifies networks as strong or weak based on controlled edge crossings. Formal definitions establish fuzzy strong-weak arcs, face memberships, dual graph constructions, and key theorems, including the 0.67 threshold that prohibits strong-strong intersections and maintains planarity values through isomorphism. Theoretical results reconcile classical Kuratowski's graphs with fuzzy gradations. The framework proves effective in the planning of the traffic network, modelling a 10 urban core intersections with vertex memberships of 0.70 - 0.90 and edge strengths revealing connectivity bottlenecks CONN limited by weak segments 5 - 10, 9 - 10 at 0.70. Strong edges form reliable backbones, while weak links identify upgrade priorities, balancing costs with necessary intersections in environments with uncertain capacities. SFPLGs provide transportation engineers with interpretable tools for durable infrastructure design, with zero-crossing embeddings verifying planarity and edge analysis guiding investments. Future work will investigate dynamic traffic data, multi-layer networks, and intuitionistic variants.

A graph G = (V,E) is well-dominated if every minimal dominating set is a minimum dominating set. That is, gamma(G) = Gamma(G). This condition may be weakened by stipulating that only non-minimal dominating sets contain minimum dominating sets. Under this condition, gamma(G) is not equal to Gamma(G) and there may exist minimal dominating sets of cardinality greater than gamma(G). Such graphs are called weakly well-dominated graphs. A study of these graphs is made in this paper.

The development of structurally diverse heterocyclic frameworks remains a cornerstone in the search for new antimicrobial agents. In this work, four sulfur-bridged heterocyclic scaffolds (S1-S4) featuring thiazole, thiadiazole, pyridine, and triazine cores were synthesized using a one-pot base-promoted nucleophilic substitution strategy facilitated by phase-transfer catalysis. Structural elucidation was achieved using spectroscopic techniques, including FT-IR, UV-Visible, H-1,C-13 NMR, and ESI mass spectrometry. Single-crystal X-ray diffraction data for scaffold S4 confirmed its symmetrical, rigid architecture. The electronic absorption spectra revealed dominant pi -> pi* transitions, consistent with high molecular planarity and delocalized electronic systems. Further insight into the electronic properties of S4 was obtained through density functional theory (DFT) calculations, which supported its extended conjugation and electron-donating potential. Antibacterial studies showed all scaffolds displayed varying inhibition against both Gram-positive and Gram-negative strains, with S4 consistently exhibiting the largest inhibition zones. Although Ciprofloxacin exhibited larger inhibition zones, the consistent measurable activity of S4 highlights it as a promising lead scaffold for future antibacterial development. The favorable performance of S4 is attributed to its highly conjugated structure and physicochemical properties, underscoring the importance of scaffold design in medicinal chemistry. Future molecular docking studies will be undertaken and correlated with in vitro antibacterial results to provide deeper insights into binding interactions and structure-activity relationships.

Exopolysaccharide-mediated silver nanoparticles (EPS-Ag2ONPs) were successfully biosynthesized using purified EPS from the marine sediment Bacillus cereus GV7. Among fourteen screened isolates, GV7 demonstrated the highest EPS production (83.7 ± 0.02 µg/mL) and was selected for Nanoparticle (NP) synthesis. EPS-Ag2ONPs were successfully synthesized under alkaline conditions, indicated by a characteristic colour change and subsequently UV-Vis spectroscopic analysis revealed a characteristic SPR peak at 424 nm. Further characterization using FTIR, SEM, EDX, XRD and AFM analysis confirmed the successful formation of spherical, well-dispersed, crystalline cubic Ag₂ONPs. SEM analysis revealed particle sizes ranging from 20 to 70 nm, whereas AFM analysis showed an average particle height of 5.09 nm. In this synthesis, EPS served as both a reducing and stabilizing agent. To our knowledge, no previous study has reported the biogenic synthesis of Ag2ONP using marine sediment-associated B. cereus GV7. Furthermore, the biosynthesized EPS-Ag2ONPs exhibited broad-spectrum antimicrobial efficacy against pathogenic microbes, with MIC values varied between 31.25 and 500 µg/mL. Significant antibiofilm activity was observed, with a maximum inhibition up to 84.54

This study presents a semi-analytical investigation of nonlinear axisymmetric flow and heat transfer of a Cross fluid over a radially stretching sheet, a configuration of considerable importance in thermofluid and polymer-processing applications. The governing nonlinear momentum and energy equations are formulated by incorporating viscoelastic and shear-thinning effects characteristic of Cross non-Newtonian fluids. An innovative application of the Rajendran–Joy method is developed to derive accurate approximate analytical solutions for the coupled transport equations. The effects of the power-law index, local Weissenberg number, and Prandtl number on velocity and temperature distributions are systematically analyzed. Variations in the local skin-friction coefficient and heat-transfer rate are also examined to elucidate the underlying transport mechanisms. The obtained analytical solutions are validated through numerical simulations performed in Matlab and by comparison with previously published results, demonstrating excellent agreement. The study highlights the efficiency, robustness, and predictive capability of the proposed methodology for solving highly nonlinear thermofluid transport problems.