http://irgu.unigoa.ac.in/drs/handle/unigoa/5 2026-07-16T17:09:07Z http://irgu.unigoa.ac.in/drs/handle/unigoa/7899 Characterizations of additively graceful signed paths and cycles D'Souza, B.; Pereira, J. A (p,m,n) signed graph S, is a signed graph of order p with m positive edges and n negative edges. In this paper, we first prove a few basic results on vertex labelings of paths. We use these results and a sequence of lemmas to obtain a characterization of additively graceful signed paths. We prove that, apart from exactly 4 exceptions, additively graceful signed paths are characterized by the signed paths containing at most one negative section with n less than or equal to 2. We also establish a characterization of additively graceful signed cycles. We prove that a (p,m,n) signed cycle S is additively graceful if and only if one among the following 4 conditions are satisfied, (a) n=0 and m identical to 0 or 3 (mod 4), (b) n = 1 and m identical to 1 or 2 (mod 4), (c) n = 2, or 2 (mod 4) and S contains a single negative section, (d) S is the all negative signed cycle on C sub(3). 2026-01-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/7841 Plasmon-enhanced fluorescence for sensitive and selective mercury ion (Hg sup(2+)) detection Bandekar, S.N.; Vij, R.; Prabhu, S.; Achanta, V.G.; Sahu, S.; Jha, R.; Sudhir, C. Plasmon-enhanced fluorescence (PEF) has emerged as an interesting platform for biosensing and quantum applications. The strong enhancement of emission from fluorophores arises due to an increase in the excitation and radiative decay rates of fluorophores in the vicinity of the metal surface. Furthermore, the excitation of surface plasmons on the metal accentuates the enhancement mechanism. A PEF-based system combines high sensitivity, photostability, and selectivity, making it a promising candidate for environmental monitoring and for the detection of trace levels of mercury ions (Hg sup(2+)) in aqueous media. Here, we report a study on PEF of CdSe-ZnS core-shell quantum dots and Rhodamine B (RhB) using silica-coated gold nanoparticles. Our observations indicate a strong enhancement in the emission intensity of these fluorophores in the vicinity of the metal nanoparticles. Along with this increase in intensity, there is a decrease in the emitter's lifetimes when mixed with the metal nanoparticles. Our study also shows that the enhancement is maximum at the plasmonic resonance wavelength, implying that this is indeed a plasmon-enhanced process. We performed finite-difference time-domain (FDTD) simulations to numerically investigate the electric-field enhancement in the immediate vicinity of silica-coated gold nanostructures and to determine the spontaneous emission characteristics of emitters. Furthermore, we use this mechanism to detect Hg sup(2+) at ultra-low levels in aqueous media. The system leverages PEF and dynamic quenching mechanisms to achieve a limit of detection (LOD) in the femtomolar (fM) range, surpassing previously reported nanocomposite-based sensors. 2026-01-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/7840 Scanning probe microscopy study of the electronic and piezoelectric properties of multilayer graphene oxide Rane, N.C.; Sudhir, C. Graphene oxide (GO), a two-dimensional material with tunable changes in electrical, electromechanical, and surface potential behavior, presents great potential for various nanoelectronic and energy-related applications. Herein, we present a detailed nanoscale study of multilayer GO flakes utilizing multimodal scanning probe microscopy (SPM) techniques, which include Conductive atomic force microscopy (C-AFM), Piezoresponsive force microscopy (PFM), and Kelvin probe force microscopy (KPFM). The C-AFM findings of multilayer GO flakes depict charge transport in the vertical direction, with the current profiles remaining relatively stable and showing no significant lateral diffusion. We interpreted this as further evidence of defined percolation pathways combined with sp sup(2)-rich conductive domains, further facilitating charge transport. Current-voltage (I-V) spectroscopic measurements indicate that the conduction mechanisms of GO samples amount to a transition from ohmic conduction to Poole-Frenkel emission, which eventually leads to dielectric breakdown and then current saturation, displaying the structural heterogeneity inherent in GO. PFM data provides an effective out-of-plane piezoelectric coefficient (d sub(33)) of approximately 0.59 pm V sup(-1) and a coercive voltage of 3V. The amplitude data indicate switchable polarization in the butterfly-shaped polarization loop, and a 180 degrees phase reversal confirms the switchable polarization behavior. The KPFM mapping verifies a surface potential of 4.80 eV, consistent with GO being a semiconductor. This work represents the multifaceted role of multilayer GO and establishes its application in nanoelectronics, energy harvesting, and memory devices. 2026-01-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/7839 MoS sub(2) Quantum Dots for Mercury Detection and Fluorescence Resonant Energy Transfer Bandekar, S.; Sudhir, C. In this work, we study the optical properties of MoS sub(2) quantum dots and utilize them for mercury ion detection using fluorimetry. Further, we utilize the overlap of the emission spectrum of MoS sub(2) and the excitation spectrum of Au nanoclusters for fluorescence resonant energy transfer. 2025-01-01T00:00:00Z