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Some new results on anti-adjacency spectra of regular graphs
The anti-adjacency matrix A*(G) of a simple graph G with V (G) = {v1,v2,v3,vn}, is a square matrix of order n with rows and columns indexed by V (G), where the (i,j)-entry (i?j) is 1, if the vertices vi and vj are not adjacent to each other and 0, otherwise. The (i,i)- entry of A*(G) is 1. The anti-adjacency eigenvalues of G are the eigenvalues obtained from the matrix A*(G) and the corresponding spectra is called the anti-adjacency spectra of G, denoted by a-spec(G). In this paper, we discuss the anti-adjacency spectra of join and disjoint union of regular graphs. The anti-adjacency spectra of bipartite regular graphs, line graphs of regular graphs and strongly regular graphs are also discussed. 2026 World Scientific Publishing Company. -
Some new results on equitable coloring parameters of graphs
An equitable coloring of a graph G is a proper vertex coloring C of G such that the cardinalities of any two color classes in G with respect to C differ by at most one. Coloring the vertices of a graph G subject to given conditions can be considered as a random experiment. In this context, a discrete random variable X can be defined as the color of a vertex chosen at random, with respect to the given type of coloring of G and a probability mass function for this random variable can be defined accordingly. In this paper, we discuss two statistical parameters of the powers of certain graph classes with respect to their equitable colorings. 2019, Univerzita Komenskeho. All rights reserved. -
Some New Results on Non-inverse Graph of a Group
The non-inverse graph corresponding to a group G, is a simple graph with vertices being elements of the group G and there is an edge between two vertices if they are not mutual inverses. In the current paper, we study few properties of the non-inverse graphs of groups. We also discuss the parameters related different types of domination no.s of the non-inverse graph. We further obtain the Laplacian spectra and signless Laplacian spectra of the non-inverse graphs. 2022 American Institute of Physics Inc.. All rights reserved. -
Some New Results on Non-zero Component Graphs of Vector Spaces Over Finite Fields
The non-zero component graph of a vector space with finite dimension over a finite field F is the graph G=(V,E), where vertices of G are the non-zero vectors in V, two of which are adjacent if they have at least one basis vector with non-zero coefficient common in their basic representation. In this paper, we discuss certain properties of the non-zero component graphs of vector spaces with finite dimension over finite fields and their graph invariants. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
Some new results on proper colouring of edge-set graphs
In this paper, we present a foundation study for proper colouring of edge-set graphs. The authors consider that a detailed study of the colouring of edge-set graphs corresponding to the family of paths is best suitable for such foundation study. The main result is deriving the chromatic number of the edge-set graph of a path, Pn+1, n ? 1. It is also shown that edge-set graphs for paths are perfect graphs. 2020 the author(s). -
Some New Results on the Rainbow Neighbourhood Number of Graphs
A rainbow neighbourhood of a graph G is the closed neighbourhood N[v] of a vertex v? V(G) which contains at least one coloured vertex of each colour in the chromatic colouring C of G. Let G be a graph with a chromatic colouring C defined on it. The number of vertices in G yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph G, denoted by r?(G). Rainbow neighbourhood number of the complements and products of certain fundamental graph classes are discussed in this paper. 2018, The National Academy of Sciences, India. -
Some notes on z-scores and t-scores /
International Journal Of Scientific Research And Management, Vol.3, Issue 4, pp.2608-2610, ISSN No: 2321-3418. -
Some pointers on one way ANOVA in spss /
International journal For Research In Applied Science And engineering Technology, Vol.3, Issue 9, pp.298-301, ISSN No: 2321-9653. -
Some properties of star-perfect graphs
For a finite simple graph G = (V, E), ?s(G) denotes the minimum number of induced stars contained in G such that the union of their vertex sets is V (G), and ?s(G) denotes the maximum number of vertices in G such that no two are contained in the same induced star of G. We call the graph G star-perfect if ?s(H) = ?s(H), for every induced subgraph H of G. We prove here that no cycle in a star-perfect graph has crossing chords and star-perfect graphs are planar. Also we present a few properties of star perfect graphs. 2026 Azarbaijan Shahid Madani University. -
Some results on b-chromatic topological indices of some graphs
Graph coloring is assigning weights, integers, or colors to edges, vertices, or both in a graph subject to certain conditions. Proper coloring C of graph G refers to assigning weights, integers, or colors to the vertices, edges, or both so that adjacent vertices or adjacent edges get a different color. A b-coloring follows proper vertex coloring with subject to an additional property that each color class should have at least one vertex with a neighbor in all the other color classes. The notion of Chromatic Zagreb index and irregularity index was introduced recently. This paper introduces the concept of b-Chromatic Zagreb indices and b-Chromatic irregularity indices. Also, we compute these indices for certain standard classes of graphs. 2023 Author(s). -
SOME RESULTS ON INJECTIVE CHROMATICS TOPOLOGICAL INDICES OF SOME GRAPHS
Graph coloring is an assignment of colors, labels or weights to the elements of graphs subject to certain conditions. Coloring the vertices of a graph G such that adjacent vertices possessing different colors is the notion of proper coloring. A proper coloring C of a graph G is called an injective coloring of G if any two vertices of G having the same neighbouring vertex have different colors in C. As a coloring analogue to Zagreb indices and irregularity indices in the literature, chromatic Zagreb and irregularity indices have been introduced very recently. In this paper, we introduce the notion of injective chromatic Zagreb indices and injective chromatic irregularity indices and determine these indices for some standard classes of graphs. 2019, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved. -
Some Variations of Domination in Order Sum Graphs
An order sum graph of a group G, denoted by ? os(G), is a graph with vertex set consisting of elements of G and two vertices say a, b? ? os(G) are adjacent if o(a) + o(b) > o(G). In this paper, we extend the study of order sum graphs of groups to domination. We determine different types of domination such as connected, global, strong, secure, restrained domination and so on for order sum graphs, their complement and line graphs of order sum graphs. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
Somnolent musings
RIGHT IN THE MIDDLE -
Sonochemical assisted impregnation of Bi2WO6 on TiO2 nanorod to form Z-scheme heterojunction for enhanced photocatalytic H2 production
In this work, Bi2WO6/TiO2 nanorod heterojunction was prepared by sonochemical assisted impregnation method. After loading 2 wt% Bi2WO6 on TiO2 nanorods, the photocatalytic hydrogen production rate of 2026 mol/h/g was achieved. Compared to commercial P25 and TiO2 nanorods, ?13 and ?3 folds enhanced activity was observed. The excellent photocatalytic performance of Bi2WO6/TiO2 nanorod photocatalyst was mainly attributed to i) reduction of bandgap due to heterojunction formation, ii) quick transport of photogenerated charge carriers, and iii) efficient charge carrier separation supported by UV-DRS, photocurrent measurement, Impedance study, and photoluminescence spectra analysis. The Z-scheme band alignment for Bi2WO6/TiO2 nanorod heterojunction was proposed based on the Mott-Schottky measurement. This result demonstrated the effective utilization of Z-scheme heterojunction of Bi2WO6/TiO2 for photocatalytic reduction application. 2021 The Society of Powder Technology Japan -
Sonographic measurement of placental volume: a comparative analysis of two-dimensional and three-dimensional sonographic techniques
To evaluate the correlation between a simple two-dimensional (2D) sonographic method and the gold-standard three-dimensional (3D) method for estimating placental volume during early to mid-pregnancy. Placental volume was measured using both 2D and 3D ultrasound techniques in 58 pregnant patients between 11 and 22 weeks of gestation. All participants had normal term pregnancy outcomes. The correlation between the two methods was analyzed using Pearson's correlation coefficient. A strong positive correlation was observed between the 2D and 3D placental volume estimates (Pearson's r=0.93, p<0.001), indicating high agreement between the two measurement approaches. The simpler 2D sonographic method shows excellent correlation with the 3D gold-standard technique and may serve as a feasible alternative for placental volume assessment, particularly in low-resource settings where access to advanced equipment is limited. 2026 the author(s) -
Soret-driven thermosolutal convection in bidispersive porous medium with vertical throughflow
This article investigates thermosolutal convection in bidispersive porous medium with Soret effect and vertical throughflow. The Oberbeck-Boussinesq approximation assumed and fluid flow obeys Darcy's law. Local thermal equilibrium is considered between solid and fluid phases. We analyze the system stability through linear instability, nonlinear stability (energy method), and weak nonlinear analysis. The expression for Ra is derived analytically, using the Galerkin orthogonalization technique. The Ginzburg-Landau equation is derived to get deep insight into convective amplitudes, also we explore the heat and mass transfer in the system by defining Nusselt and Sherwood numbers. The research delves into the influence of various physical parameters on the system's stability. The solutal Rayleigh number and Soret number have destabilizing property, whereas the Lewis number, momentum transfer coefficient, and permeability ratio have the stabilizing nature. The sub-critical region decreases as the Soret number increases. The strong buoyancy force delays the heat transfer and mass transfer by disrupting existing mass transfer. The critical Rayleigh number maintains symmetry over the upward and downward throughflow. The less area under the curve for average Nusselt and Sherwood number over permeability ratio implies total heat and mass transfer alleviating. 2025 Author(s). -
Source-load-variable voltage regulated cascaded DC/DC converter for a DC microgrid system
Solar energy is available abundantly, the utilization of solar energy is developing rapidly and the photovoltaic based direct current (DC) microgrid system design is under demand but the stability of the DC voltage is of most important issue, as the variation of the output DC voltage is a common problem when the load or source voltage varies, hence a regulated DC output voltage converter is proposed. This paper presents source-load-variable (SLV) voltage regulated cascaded DC/DC converter which is used to obtain regulated output voltage of 203.1 V DC at 0.4 duty ratio with 2% voltage fluctuations for the variation in the input source voltage and 1.5% voltage fluctuations for the variation in load resistance of the nominal value with lower output voltage ripple and without use of sub circuits. A simulation model of SLV voltage regulated cascaded DC/DC converter in LTspice XVII software environment for the assessment of converter performance at different input source voltages and load resistances are verified. 2023 Institute of Advanced Engineering and Science. All rights reserved. -
Space taxonomy: Need for a progressive tax regime
Konstantin Tsiolkovsky famously stated that while the Earth serves as the birthplace of humanity, it is not a place where mankind can indefinitely remain. Perhaps during that period, the prospect of exploring the mysteries of outer space appeared to be an unattainable aspiration. However, in the present day, there are no longer any limitations, not even the sky, since human ingenuity has facilitated access to outer space for humanity. This access is not just for the purposes of research and exploration but also for economic endeavours. Until now, the commercial utilisation of outer space has advanced at a very sluggish rate. However, firms including SpaceX, Orion Span, Virgin Galactic, and Blue Origin have achieved significant advancements in the growth of the space industry. The revenue generated by various space-related endeavours has experienced a significant 73% increase over the last ten years. The global space economy, estimated to be valued at USD one trillion in the coming years, is primarily driven by commercial activities. This presents a formidable challenge to the existing national and international taxation systems. Similar to the open seas, space is also considered res communis omnium, meaning it belongs to the entire community, and presents comparable taxing challenges with potentially uncertain solutions. The three fundamental elements of every taxation regulation, such as the Organisation for Economic Co-operation and Development or the United Nations Model Double Taxation Convention, are the taxpayer's place of residence, the origin of their income, and the methods by which they generate their money. The current tax system does not have the necessary concepts and provisions to adapt to the rapid advancements in commercial space technology. This paper examines the legal issues surrounding commercial activities conducted in space, including the nature and handling of the income generated in various legal systems. It also addresses concerns such as tax avoidance and excessive taxation, emphasising the necessity for a globally coordinated approach to effectively tax commercial activities in space. 2024 -
Spanning graph topology of graphs
The collection of subgraphs of a graph G containing G and the null graph K0, which is closed under union and intersection, is said to be a graph topology defined on G. In this paper, we investigate the idea of spanning graph topology of a graph G, where we consider the collection of spanning subgraphs of G satisfying the axioms analogous to the axioms of graph topology. We begin with the basic concepts of spanning graph topological space and later and introduce two spanning subgraph complements to define closed graphs in spanning graph topological spaces. 2023 World Scientific Publishing Company. -
Spatial analysis of CO poisoning in high temperature polymer electrolyte membrane fuel cells
The improved tolerance of the High Temperature-Polymer Electrolyte Membrane Fuel Cell (HT-PEMFC) to CO allows the use of reformate as an anode feed. However, the presence of several per cent of CO in the reformate, which is inevitable particularly in on-board reformation in automobiles, which otherwise demands complex systems to keep the CO level very low, will significantly lower the cell performance, especially when the HT-PEMFC is operated at 160 C or below. In this study, a three-dimensional, non-isothermal numerical model is developed and applied to a single straight-channel HT-PEMFC geometry. The model is validated against the experimental data for a broad range of current densities at different CO concentration and operating temperatures. A significant spatial variation in current density distribution is observed in the membrane because the CO sorption is a spatially non-homogeneous process depending on local operating conditions and dilution of the H2 stream. To investigate the local spatial effects on HT-PEMFC operation, the model is applied to a real cell of size 49.4 cm2 with an 8-pass serpentine flow-field at the anode and the cathode. The membrane and anode catalyst layer are segmented into 5 array to investigate the spatial resolution of the polarization curves, H2 concentration, current density, and anode polarization loss. The simulation results show that the presence of CO in the anode feed reduces cell performance, however, the results reveal that uniformity in current density distribution in the membrane improves when the cell is operated in potentiostatic mode. The results are discussed in detail with the help of several line plots and multi-dimensional contours. The study also emphasizes on the importance of optimizing the reformate anode feed rate to improve cell performance. 2020 Hydrogen Energy Publications LLC