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On Leech labelings of graphs and some related concepts
Let G=(V,E) be a graph and let f:E?{1,2,3,} be an edge labeling of G. The path weight of a path P in G is the sum of the labels of the edges of P and is denoted by w(P). The path number of G, tp(G) is the total number of paths in a graph G. If the set of all path weights S in G with respect to the labeling f is {1,2,3,,tp(G)}, then f is called a Leech labeling of G. A graph which admits a Leech labeling is called a Leech graph. Leech index is a parameter which evaluates how close a graph is towards being Leech. In this paper, the path number of the wheel graph Wn is obtained. We also determine a bound for the Leech index of Wn and a subclass of unicyclic graphs. A python program that gives all possible Leech labelings of a cycle Cn for n?3, if it exists, is also provided. 2023 Elsevier B.V. -
On m-quasi Einstein almost Kenmotsu manifolds
In this article, we consider m-quasi Einstein structures on two class of almost Kenmotsu manifolds. Firstly, we study a closed m-quasi Einstein metric on a Kenmotsu manifold. Next, we proved that if a Kenmotsu manifold M admits an m-quasi Einstein metric with conformal vector field V, then M is Einstein. Finally, we prove that a non-Kenmotsu almost Kenmotsu (?,?)' -manifold admitting a closed m-quasi Einstein metric is locally isometric to the Riemannian product Hn+1Rn, provided that ?-?(2n+m)/2m = 1. 2021 Universita degli Studi di Parma. All rights reserved. -
ON SECOND HYPER-ZAGREB INDEX OF CORONA PRODUCTS RELATED TO R-GRAPHS
The cognitive and evidential features of the graph discipline are significantly influenced by the implementation of graph operations. Molecular descriptor acts as a fundamental network invariant relevant to a particular molecular structure in the framework of chemical graph theory. The semi-total point graph features the edges of subdivision graph as well as the edges of the original graph. In this paper, we explore combinatorial inequalities associated with the edges, vertices and its corresponding neighborhood notions along with the inclusion of other molecular descriptors in the computations for the determination of exact expressions of second hyper-Zagreb index for certain corona products involving the semi-total point graph. 2023 Academic Publications -
On the differential transform method of solving boundary eigenvalue problems: An illustration
The differential transform method (DTM) is a simple technique based on the Taylor series. Applying the DTM, a given linear boundary eigenvalue problem (BEVP) involving ordinary differential equations is converted into a recurrence relation or a system of recurrence relations for the Taylor coefficients. This ultimately leads to the solution of the problem in the form of an infinite power series with an appropriate region of convergence. The present paper aims to apply the DTM in solving a BEVP arising from the DarcyBrinkman convection in a rectangular box subject to general boundary conditions whose vertical sidewalls are assumed to be impermeable and adiabatic. The non-dimensional temperature difference between the plates represented by the DarcyRayleigh number, the eigenvalue of the problem, is obtained as a function of the width of the Bard cell ((Formula presented.) : b is the horizontal wave number) and other parameters using the DTM. The work includes investigation on the convergence of the series solution. The solution by the DTM is compared with that obtained by the MATLAB bvp4c routine and excellent agreement is found thereby establishing the accuracy of theDTM. 2020 Wiley-VCH GmbH -
On the discrete weibull marshallolkin family of distributions: Properties, characterizations, and applications
In this article, we introduce a new flexible discrete family of distributions, which accommo-dates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets. 2021 by the authors. Licensee MDPI, Basel, Switzerland. -
ON THE GENERALIZED COMPLEMENT OF SOME GRAPHS
In this paper we study the generalized complement of the graph Gm,n = (V, E) for some values of m, n. We study the generalized complement of Gm,n graphs with respect to the equal degree partition. The 2?complement of Gm,n graphs are also determined for m = 2, n is even or odd. In particular, for some values of m, n ? N, we studied the complement of Gm,n graphs with respect to the equal degree partition and the 2?complement of Gm,n graphs. We determine the partitions Pk, k ? N of the vertex set V such that the generalized complement of Gm,n graph is a path graph and a comb graph. 2021, Asia Pacific Academic. All rights reserved. -
On the Hermite and Mathieu Special Characterizations to the Logarithmic ZakharovKuznetsov Equations
In this paper, we find the new travelling wave solutions for several aspects of logarithmic ZakharovKuznetsov (ZK) equations using an efficient technique called the special function method which is composed of Hermite and Mathieu differential equations being novel and special functions. In order to illustrate the efficiency of the projected scheme, we considered four different examples with different cases, namely, logarithmic ZK (log-ZK) equation, logarithmic modified ZK (log-mZK) equation, and logarithmic ZK modified equal width (log-ZK-mEW) equation and logarithmic ZKBenjaminBonaMahony (log-ZKBBM) equation. The behaviour of the obtained results and corresponding consequences are illustrated and captured. Finally, the obtained results confirm that the considered solution procedure can be widely employed to find the solution and also capture some interesting and stimulating consequences. 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited. -
ON THE INDICES OF CERTAIN GRAPH PRODUCTS
Molecular descriptors are numerical graph invariants that are used to study the chemical structure of molecules. In this paper, we determine the upper bound of the Sombor index based on four operations involving the subdivision graph, semi-total point graph, semi-total line graph, and total graph related to the lexicographic and tensor product. The exact expressions of the first reformulated Zagreb index and the second hyper-Zagreb index of the tensor product are formulated on the basis of the four significant graphs. Further, the descriptors for certain standard graphs are obtained and the graphical comparison for the first reformulated Zagreb index has also been illustrated to understand the result better. 2025 University of Isfahan -
On the Mass Accretion Rate and Infrared Excess in Herbig Ae/Be Stars
The present study makes use of the unprecedented capability of the Gaia mission to obtain the stellar parameters such as distance, age, and mass of HAeBe stars. The accuracy of Gaia DR2 astrometry is demonstrated from the comparison of the Gaia DR2 distances of 131 HAeBe stars with the previously estimated values from the literature. This is one of the initial studies to estimate the age and mass of a confirmed sample of HAeBe stars using both the photometry and distance from the Gaia mission. Mass accretion rates are calculated from H? line flux measurements of 106 HAeBe stars. Since we used distances and the stellar masses derived from the Gaia DR2 data in the calculation of the mass accretion rate, our estimates are more accurate than previous studies. The mass accretion rate is found to decay exponentially with age, from which we estimated a disk dissipation timescale of 1.9 0.1 Myr. The mass accretion rate and stellar mass exhibit a power-law relation of the form . From the distinct distribution in the values of the infrared spectral index, n2-4.6, we suggest the possibility of difference in the disk structure between Herbig Be and Herbig Ae stars. 2019. The American Astronomical Society. All rights reserved.. -
On the Motion of Non-Newtonian EyringPowell Fluid Conveying Tiny Gold Particles Due to Generalized Surface Slip Velocity and Buoyancy
In the painting industry, space science and biomedical science, the nature of relaxation in the flow of non-Newtonian fluid (i.e. blood) containing gold (Ag) suits the characteristics of EyringPowell fluid flow induced by generalized surface slip velocity and buoyancy. However, flow of various non-Newtonian fluids on the horizontal surface of a slanted paraboloid of revolution objects (i.e. rocket, as in space science), over a bonnet of a car and over a pointed surface of an aircraft is of importance to experts in all these fields. In this article, the analysis of the motion within the thin layer formed on a horizontal object which is neither a perfect horizontal nor vertical and neither an inclined surface nor a cone/wedge is presented. The transformed governing equations which model the flow was non-dimenzionalized, parameterized and solved numerically using a well-known RungeKutta integration procedure along with shooting technique. The influence of increasing the magnitude of major parameters on the temperature distribution, local heat transfer rate, concentration of the fluid, local skin friction coefficient and velocity of the flow are illustrated graphically and discussed. Velocity slip parameter is found to be a decreasing function of temperature distribution across the flow. Heat transfer rate (NuxRex-1/2) at the wall (?= 0) is an increasing function of velocity slip parameter. Maximum coefficient of concentration of homogeneous bulk fluid at the wall exists at larger values of the emerged velocity slip and volume fraction parameters. 2018, Springer Nature India Private Limited. -
On the Non-Inverse Graph of a Group
Let (G, ?) be a finite group and S = {u G|u u-1}, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u ? v S or v ? u S. In this paper, we introduce a modified version of the inverse graph, called i?-graph associated with a group G. The i?-graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ? are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i?-graph are also determined. 2022 Javeria Amreen et al., published by Sciendo. -
On the quick estimation of probability of recovery from COVID-19 during first wave of epidemic in India: a logistic regression approach
The COVID-19 pandemic has recently become a threat all across the globe with the rising cases every day and many countries experiencing its outbreak. According to the WHO, the virus is capable of spreading at an exponential rate across countries, and India is now one of the worst-affected country in the world. Researchers all around the world are racing to come up with a cure or treatment for COVID-19, and this is creating extreme pressure on the policy makers and epidemiologists. However, in India the recovery rate has been far better than in other countries, and is steadily improving. Still in such a difficult situation with no effective medicine, it is essential to know if a patient with the COVID-19 is going to recover or die. To meet this end, a model has been developed in this article to estimate the probability of a recovery of a patient based on the demographic characteristics. The study used data published by the Ministry of Health and Family Welfare of India for the empirical analysis. Hemlata Joshi, S. Azarudheen, M. S. Nagaraja, Singh Chandraketu. -
On the rainbow neighbourhood number of Mycielski type 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 colored vertex of each color in the chromatic coloring C of G. Let G be a graph with a chromatic coloring 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 rX(G). In this paper, we discuss the rainbow neighbourhood number of the Mycielski type graphs of graphs. 2018 Academic Publications. -
On the rainbow neighbourhood number of set-graphs
In this paper, we present results for the rainbow neighbourhood numbers of set-graphs. It is also shown that set-graphs are perfect graphs. The intuitive colouring dilemma in respect of the rainbow neighbourhood convention is clarified as well. Finally, the new notion of the maximax independence, maximum proper colouring of a graph and a new graph parameter called the i-max number of G are introduced as a new research direction. 2020 the author(s). -
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 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 Πk – connectivity of some product graphs
Vol. 21, No.2, 70 - 79 ISSN 13105132