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ON THE SECURE EQUITABLE DOMINATION IN GRAPHS
A secure equitable dominating set S of a graph G is a dominating set in which for any vertex v ? V (G) \ S there exists at least one vertex u ? S such that u ? Ne(v), where Ne(v) indicate the equitable neighbourhood of v, and if we swap the vertex u with v, the equitable domination property of the graph will be unharmed. ?esec(G) represents the secure equitable domination number of G, which is the cardinality of the minimum secure equitable dominating set in G. The improved bounds of the secure equitable domination number of some fundamental kinds of graphs are established in this study. Furthermore, we incorporate specific results based on the diameter, girth, and degree. Additionally, we determine the bounds of the secure equitable domination number of specific special classes of graphs. I??k University, Department of Mathematics, 2025; all rights reserved. -
On the secure vertex cover pebbling number
A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely, secure vertex cover and cover pebbling number, is introduced in this paper. The secure vertex cover pebbling number of a graph, G, is the minimum number m so that every distribution of m pebbles can reach some secure vertex cover of G by a sequence of pebbling moves. In this paper, the complexity of the secure vertex cover problem and secure vertex cover pebbling problem are discussed. Also, we obtain some basic results and the secure vertex cover pebbling number for complete r-partite graphs, paths, Friendship graphs, and wheel graphs. 2023 World Scientific Publishing Co. Pte Ltd. All rights reserved. -
On the Temporal Causal Relationship Between Macroeconomic Variables: Empirical Evidence From India
The present study examines the dynamic interactions among macroeconomic variables such as real output, prices, money supply, interest rate (IR), and exchange rate (EXR) in India during the pre-economic crisis and economic crisis periods, using the autoregressive distributed lag (ARDL) bounds test for cointegration, Johansen and Juselius multivariate cointegration test, Granger causality/Block exogeneity Wald test based on Vector Error Correction Model, variance decomposition analysis and impulse response functions. The empirical results reveal a stronger long-run bilateral relationship between real output, price level, IR, and EXR during the pre-crisis sample period. Moreover, the empirical results confirm a unidirectional short-run causality running from price level to EXR, IR to price level, and real output to money supply during the pre-crisis period. Also, it is evident from the test results that there exist short-run bidirectional relationships running between real output and EXR, price level and IR, and IR and EXR in the pre-crisis era, respectively. Most importantly, long-run bidirectional causality is found between real output, EXR, and IR during the economic crisis period. And the study results indicate short-run bidirectional causality between money supply and EXR, IR and price level, and IR and output in India during the crisis era. Also, a short-run unidirectional causality runs from prices to real output in the crisis period. The Author(s) 2014. -
On the Wave Propagation and Dynamic Response of a Spherical Cavity in Piezoelectric Microstructures via Rabotnov Kernel-Based MooreGibsonThompson Thermoelasticity Theory
This study investigates the transient dynamic response and thermomechanical stability of a transversely isotropic piezoelectric medium featuring a spherical cavity. To accurately model the small-scale effects inherent in advanced structural components, a spatiotemporal nonlocal elasticity framework of the KleinGordon type is employed, incorporating both internal length and intrinsic time scale parameters. The governing equations of the MooreGibsonThompson (MGT) thermoelastic model are reformulated using a nonsingular Rabotnov-type fractional exponential kernel, providing a robust mathematical formulation to capture memory-dependent interactions without the paradox of infinite propagation speeds. The structural boundary of the cavity is subjected to a ramp-type thermal loading and electrical grounding, simulating realistic operational conditions for sensors and actuators. Using the Laplace transform technique and the Zakian numerical inversion method, the transient distributions of temperature, displacement, stress, and electric potential are derived. The results highlight the significant influence of the Rabotnov fractional parameter and spatiotemporal nonlocality on the structural stability and wave-front characteristics. This research provides a unique medium for understanding the latest developments in fractional-order dynamics for piezoelectric micro- and nano-structures, offering practical insights for civil, aerospace, and mechanical engineering applications. 2026 World Scientific Publishing Company. -
On the zero forcing number of complementary prism graphs
The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph G. The aim of this article is to compute the zero forcing number of complementary prism graphs. Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result. Let G and ? be connected graphs. Then Z(G?) ? n ? 1 if and only if there exists two vertices vi, vj ? V (G) and i 6? j such that, either N(vi) ? N(vj) or N[vi] ? N[vj] in G. 2025 Azarbaijan Shahid Madani University. -
On the zero forcing number of graphs and their splitting graphs
In [10], the notion of the splitting graph of a graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph ? of order n ? 2, Z[S(?)] ? 2Z(?) and also obtain many classes of graph in which Z[S(?)] = 2Z(?). Further, we show some classes of graphs in which Z[S(?)] < 2Z(?). Journal Algebra and Discrete Mathematics. -
On thermal performance of spine fin in magnetized hybrid fluid rooted with Cu and MoS4 nanoparticles
This study examines the thermal performance of diverse profiles of spine fins with variable thermal conductivity. A hybrid nanofluid comprising Cu, and MoS4 with water as the base fluid, is modeled mathematically. Both the cylindrical and concave parabolic profiles are taken into account. The comparative outcomes are inferred from numerical and semi-analytical methods. The non-dimensional temperature profiles are analyzed graphically while considering the fin tip to be insulated, and the effects of various thermal parameters are also investigated. We have observed that the heat transfer rate shows an opposite trend toward convective-conduction and porosity parameter. The study also revealed that the concave parabolic profile emits more heat in comparison with the cylindrical profile. 2024 Author(s). -
ON TRANSFORMED GRAPHS
The network systems and graphical analysis through the study of structural characteristics is a vast field of growing importance in research. Topological indices have a significant and crucial role in the study of structureproperty relationships. In this paper, we examine constructional transformed networks constructed by unique vertex-edge incidence and mutual adjacency associations. Expressions for the first and second hyper Zagreb indices and co-indices of these transformed networks and their complements are obtained. 2023, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved. -
On Two-Dimensional Approximate Pattern Matching Using Fuzzy Automata
Pattern matching has been extensively studied in the last few decades, owing to its great contribution in various fields such as search engines, computational biology, etc. Several real-life situations require patterns that allow ambiguity in specified positions. In this paper, one-dimensional and two-dimensional approximate pattern matching models have been constructed using fuzzy automata. The similarity function used in fuzzy automata enables the occurrence of all exact and similar one-dimensional and two-dimensional patterns. This kind of searching approximate patterns is not possible with regular search models. The time complexity of the proposed algorithm has also been analyzed. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024. -
On Πk – connectivity of some product graphs
Vol. 21, No.2, 70 - 79 ISSN 13105132 -
On-board Converter for Electric Vehicle Charging using LCLC Resonant Topology
Due to their high efficiency, high power density, and soft switching characteristics, LLC-based AC-DC resonant converters are a great choice for EV chargers. Adding a capacitor across the magnetizing inductance of the LLC resonant architecture (LCLC configuration) enhances efficiency and reduces the need for a larger series inductor. The output DC voltage of the converter is generally regulated using switching frequency control. However, the power factor of the converter varies significantly with the switching frequency. As a result, any fluctuations in load may cause the converter to operate at a lower power factor. This paper proposes a single-stage topology based on the LCLC resonant structure. Zero voltage switching (ZVS) of the IGBTs used in the converter is ensured by the LCLC resonant configuration. Converter have a power factor correction (PFC) stage on the front of the converter to achieve natural power factor correction. Since the PFC stage and the resonant stage are controlled by the same switches, the converter is smaller and less costly. Simulations in MATLAB/Simulink are used to validate the topology. 2023 IEEE. -
On-off fluorescence detection of exposed phosgene via pyrazine ring formation on a triphenyl amine backbone supplemented with a theoretical approach and practical environmental applications
Using 4-(diphenylamino)benzaldehyde as the fluorophore and 2,3-diaminomaleonitrile, a fluorescent probe known as 2-amino-3-(((E)-4-(diphenylamino)benzylidene)amino)-maleonitrile (ADM) has been developed for the selective detection of phosgene through a unique cyclization pathway producing a substituted pyrazine derivative attached to a triphenyl amine backbone. This reaction led to a notable reduction in the emission intensity of ADM at 565 nm. This is the first study that reports ADM as a sensory material for the selective detection of phosgene, achieved by forming a new heterocyclic pyrazine structure. With a quick response time of only 80 seconds, the detection limit of the probe ADM towards phosgene has been calculated as 4.23 ?M. Several spectroscopic methods, including UV-vis, emission spectroscopy, mass spectrometry, and computational investigations are used to study the sensing behavior. In practical applications, the sensor ADM can be used for soil analysis, the dipstick method, and the detection of phosgene from chlorinated hydrocarbon sources such as dichloromethane, chloroform and household solvents like paint remover. 2024 The Royal Society of Chemistry. -
One dimensional NiMn2O4 nanofibrous architectures for symmetric supercapacitor device
In this study, NiMn2O4 nanofibers are synthesized using an electrospinning method. The NiMn2O4 nanofiber films, coated on stainless-steel substrates, are electrochemically characterized in different electrolytes, including KCl, KOH, NaOH, and Na2SO4. The study explores how the choice of electrolyte influences the specific capacitance, galvanostatic charge-discharge behavior, cycle stability, and capacitance retention of the NiMn2O4 nanofiber electrodes. NiMn2O4 electrodes in KOH exhibit superior performance at a scan rate of 5 mV/s, with an areal capacitance of 2125 F/g. The higher capacitance in KOH is attributed to its high ionic conductivity and efficient ion mobility. Additionally, the NiMn2O4 nanofiber electrodes demonstrate excellent cycle stability, with 76.38 % capacitance retention in 1 M KOH. These results suggest that 1D NiMn2O4 nanofiber electrodes deliver superior electrochemical performance in KOH compared to other aqueous electrolytes, highlighting their potential for future electrochemical energy storage applications. Furthermore, the flexible symmetric supercapacitor device shows excellent flexibility and electrochemical stability, with specific energy of 660 Wh/kg and specific power of 140 kW/kg obtained at a current density of 2 mA/cm2. These findings indicate that 1D NiMn2O4 nanofibers, particularly in 1 M KOH, are promising candidates for high-performance supercapacitor applications, paving the way for advancements in electrochemical energy storage devices. 2025 Elsevier B.V. -
One Pot Hydrothermal Synthesis and Application of Bright-yellow-emissive Carbon Quantum Dots in Hg2+ Detection
Carbon quantum dots (CQD) have drawn great interest worldwide for their extensive application as sensors due to their extraordinary physical and chemical characteristics, good biocompatibility, and high fluorescence in nature. Here, we demonstrate a technique for detecting mercury (Hg2+) ion using a fluorescent CQD probe. Ecology is concerned about the accumulation of heavy metal ions in water samples due to their harmful effects on human health. Sensitive identification and removal of metal ions from water samples are required to reduce heavy metals risk. To find out Mercury in the water sample, carbon quantum dots were used and synthesized by 5-dimethyl amino methyl furfuryl alcohol and o-phenylene diamine through the hydrothermal technique. The synthesized CQD shows yellow emission when exposed to UV irradiation. Mercury ion was used to quench carbon quantum dots, and it was found that the detection limit was 5.2 nM with a linear range of 15100 M. The synthesized carbon quantum dots were demonstrated to efficiently detect Mercury ions in real water samples. 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. -
One pot synthesis of a novel bioactive compound employing a deep eutectic solvent grafted MWCNT system in a solventless environment
Heterogeneous catalysis is considered as a suitable alternative to conventional organic synthesis for the selective production of industrially significant fine chemicals. The development of supported catalysts by dispersing minimal quantities of active component can reduce production costs and enhance energy efficiency. The current work reports the development of Deep eutectic solvent (DES) modified multiwalled carbon nanotube (MWCNT) system and its activity in the Knoevenagel condensation reaction. The catalytic system was developed by grinding a very low concentration (0.83mM) of DES with desired amount of MWCNT. Various interactions of the three component DES with MWCNT were analysed by X-ray photoelectron spectroscopy (XPS). The reaction favoured a novel compound selectively with yield around 92% in solvent free medium. Anti-cancerous studies of the synthesized compound demonstrated a strong IC50 value of 15.62g/ml and a statistically calculated IC50 value of 9.8g/ml. Acridine orange/ Ethidium Bromide (AO/EB) dual fluorescence staining studies revealed that the test ligand with lowest concentration of 7.8g/ml was capable to induce apoptosis in 100% of MCF-7 cells. It is evident from the studies that the synthesized compound is a strong anticancer agent with potential to be investigated further. The Author(s) 2025. -
One Time Password-Based Two Channel Authentication MechanismUsing Blockchain
Using Fog Nodes, also known as IOT devices are increasing everyday with more and more home automation, industry automation, automobile automation, etc. Security threats for these devices are also increasing. One of the threats is impersonating one fog node, stealing data and taking control of the network which is also known as the Sybil attack. To provide security, most fog devices use one step or two step authentication and sometimes use encryption. With static passwords, there is a chance of compromise by password sharing and leaking. Some weak encryption algorithms used are also compromised. Data about fog nodes in the network is stored in a weak database and is tampered. OTP-based Two Channel Authentication Mechanism (OTPTAM) to authenticate the fog nodes with metadata stored in Blockchain Database and communicate using channels encrypted with Elliptical Ciphers can solve the majority of these problems. Metadata of the nodes like Bluetooth MAC address, network mac address, telephone number are all stored in the blockchain and the OTP is exchanged via these channels to ensure the authenticity of the fog nodes. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
One-pot hydrothermal synthesis of 3D garland BiOI, spherical ZnO, and CNFs onto Ni foam: Supercapacitor performance with enhanced electrochemical properties
This study reported one-pot hydrothermal synthesis of 3D garland BiOI, spherical ZnO, and carbon nanofibers (CNFs) onto Ni foam substrate with improved supercapacitor performance and enhanced electrochemical properties. The synthesized nanocomposites exhibited high specific capacitance (SC) of 1073 g?1 at a current density of 1 A/g and excellent cycling stability with 88.6% retention of original capacity after 5000 cycles in 2M KOH aqueous solution. The findings highlight the potential of 3D materials for use as electrode materials in advanced supercapacitor applications due to their high energy storage capabilities. 2024 Elsevier Ltd -
One-pot hydrothermal synthesis of MWCNTs/NiS/graphitic carbon nitride as next generation asymmetric supercapacitors
Fabricating new electrode materials with high capacitive properties is crucial in contemporary research. The construction of hybrid supercapacitors developed using transition metal-sulfides and carbonaceous materials provides significant surface area and distinctive charge storage characteristics. In the present work, NH2-multiwalled carbon nanotubes/NiS/g-C3N4 (MNG) hybrid was synthesized by a one-pot hydrothermal method, and pristine g-C3N4 using thermal method. The morphological studies of the hybrid materials show the presence of tube like MWCNTs, sphere-like NiS, and sheet like g-C3N4. The uniform distribution of all the components in the hybrid helps in exhibiting excellent electrochemical performances. The prepared electrode material shows a specific capacitance of 2432 F g?1 at a current density of 4 A g?1. Furthermore, following a series of 10,000 cycling tests, the hybrid ternary composite retains 98 % of its initial capacitance. An asymmetric coin cell of MNG//AC was fabricated with an exceptional energy density of 73.3 Wh kg?1 and a power density of 1599.2 W kg?1. This remarkable rate performance and cycle stability exhibited by the material indicate its potential as a highly efficient electrode material for supercapacitors. 2024 Elsevier B.V. -
One-pot sustainable synthesis of novel pyrido[2,3-d]pyrimidinones and their evaluation for antitubercular and anticancer activity
A novel green protocol for the construction of diversified pyrido[2,3-d]pyrimidinones was accomplished by a single-pot reaction of aryl aldehydes, Meldrum's acid, thiobarbituric acid, and ammonium acetate/aniline in H2O using ?-proline as an expeditious reusable catalyst at room temperature (26 C). Our strategy provides an innovative synthetic avenue for the construction of pyrido[2,3-d]pyrimidinones, as well as several advantages over traditional methods, including a simple procedure, shorter reaction duration, excellent yields, safe handling, easy workup, catalyst recovery, and environmental compatibility. Furthermore, the synthesised compounds were tested for their impact on different cell lines and microorganisms. Compounds 5d and 5e were particularly effective against Mycobacterium tuberculosis (antitubercular), human breast cancer cells (MCF-7), lung cancer cells (A549 and NCI-H460), and both Gram-positive (S. pyogenes) and Gram-negative (E. coli) bacteria. The derivatives with hydroxyl and nitro substitutions [5e, 5f] showed the highest potency against MCF-7, A549, and NCI-H460 cell lines, with IC50 values of 3.684.36, 3.823.41, and 11.3412.28 g/mL, respectively. 2024 The Author(s) -
One-pot sustainable synthesis of novel pyrido[2,3-d]pyrimidinones and their evaluation for antitubercular and anticancer activity
A novel green protocol for the construction of diversified pyrido[2,3-d]pyrimidinones was accomplished by a single-pot reaction of aryl aldehydes, Meldrum's acid, thiobarbituric acid, and ammonium acetate/aniline in H2O using ?-proline as an expeditious reusable catalyst at room temperature (26 C). Our strategy provides an innovative synthetic avenue for the construction of pyrido[2,3-d]pyrimidinones, as well as several advantages over traditional methods, including a simple procedure, shorter reaction duration, excellent yields, safe handling, easy workup, catalyst recovery, and environmental compatibility. Furthermore, the synthesised compounds were tested for their impact on different cell lines and microorganisms. Compounds 5d and 5e were particularly effective against Mycobacterium tuberculosis (antitubercular), human breast cancer cells (MCF-7), lung cancer cells (A549 and NCI-H460), and both Gram-positive (S. pyogenes) and Gram-negative (E. coli) bacteria. The derivatives with hydroxyl and nitro substitutions [5e, 5f] showed the highest potency against MCF-7, A549, and NCI-H460 cell lines, with IC50 values of 3.684.36, 3.823.41, and 11.3412.28 g/mL, respectively. 2024 The Author(s)