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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 Maximization of Some Graph Coloring Problems
A graph coloring problem involves labeling the vertices or edges in a graph with newlinecolors or numbers subject to some constraints. The most frequently known graph newlinecoloring problems are the ones that usually minimize the number of colors used in newlinecoloring the vertices or edges. The chromatic number of a graph G, denoted by and#967;(G), is the least number of colors used in a proper coloring of G. The chromatic sum of a graph G, denoted as P(G), was introduced in [1], which is to and the smallest possible coloring sum in a proper coloring of the graph G using natural numbers. Lately, a few studies have endured in a distinct area of the literature where the number of colors used in a graph coloring problem is maximized under certain conditions. Some of these works have applications in network sciences. newlineThe concerned study focuses on the maximization of three dierent edge coloring newlineconcepts, viz., the vertex induced kand#8722;edge coloring, vertex incident kand#8722;edge coloring, newlineand edge incident 2and#8722;edge coloring of a simple connected graph G, where k and#8805; 2. The newlinenumber of colors assigned to the edges of the graph G has been maximized under certain conditions. The vertex induced kand#8722;edge coloring and the vertex incident newlinekand#8722;edge coloring concepts are the generalized version of the edge coloring approach newlineintroduced and studied in [2]. Furthermore, the concept of the achromatic sum of a graph G has also been introduced here. This concept is to and the greatest possible coloring sum of the graph G in an improper edge coloring using natural numbers. An extensive study newlineon three achromatic sums, namely the vertex induced 2and#8722;edge coloring sum, the vertex incident 2and#8722;edge coloring sum, and the edge incident 2and#8722;edge coloring sum are carried out. A few bounds for these parameters on a simple connected graph G and the exact values for some elementary graph classes have been investigated. A few comparative results between some of these parameters have also been obtained. -
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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 Laplacian energy of interval valued fuzzy graphs
Interval valued fuzzy Laplacian matrix (IVFLM) associated with an interval valued fuzzy graph (IVFG) is studied in this paper. We define spectrum, energy, Laplacian spectrum and Laplacian energy and obtain some bounds for energy and Laplacian energy. 2020 Author(s). -
On the k-Forcing Number of Some DS-Graphs
Amos et al. introduced the notion of k-forcing number as a generalization of Zero forcing number and is denoted by Fk(G) where k> 0 is any positive integer, the k -forcing number of a graph is the minimum cardinality among all k -forcing sets of a graph G. In this paper, many bounds for k -forcing number of degree splitting graph DS(G) for different graph classes are found. We evaluate the value of k -forcing number of degree splitting graph of some of the Cartesian product graph for different values of k. Also we observed that for Tur graph Tn , t, upper and lower bound is given by, Fk(Tn , t) ? Fk(DS(Tn , t) ) ? Fk(Tn , t) + 1. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
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 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 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 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 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 Statistical Tools in Finding Equitable Antimagic Labeling of Complete Graphs
Graph theory is a branch of mathematics that deals with representation of graphs with vertices and edges. Graph labeling is the assignment of integer labels to either vertices or edges. For a given graph G= (V, E), an edge-weighting is a function f:E(G)?{1,2,3,..,|E(G)|}. For a vertex v of G, let Wf(v) denotes the sum of edge-weights appearing on the edges incident at v under the edge-weighting f. A bijective edge-weighting f of G is said to be an equitable antimagic labeling (EAL) of G if |Wf(u) - Wf(v) | ? 1 for any pair of adjacent vertices u and v of G. A graph admitting an EAL is called an equitable antimagic graph (EAG). In this paper, the characterization of complete graphs Kn, for n? 6 is dealt using an algorithmic approach. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
On Specific Properties Common to a Graph and its Complement
In this dissertation we study some specific properties common to a graph and its complement. Here we compare the independence number of a graph with the chromatic number of its complement and find some relation between these properties for cycle, path, wheel, Berge graph, star and for some other graphs. We also find the relation between the independence number of a graph and its complement with its order. -
On some properties of partial dominating sets
A subset of the vertex set of a graph is a dominating set of the graph if that subset and all the adjacent vertices of that subset form the whole of the vertex set. In case, if a subset and all the adjacent vertices of that subset form part of the whole set, say, for 0 < p < 1, ptimes of the whole vertex set, we say it is a partial domination. In this paper, we explore some of the properties of partial dominating sets with respect to particular values of p. 2020 Author(s). -
On Some Graphs Whose Domination Number Is thePerfect Italian Domination Number
Perfect Italian Domination (PID) is a vertex labelling of a graph G by numbers from the set such that a vertex in G labelled 0 has a neighbourhood where the summation of the labels of the vertices in it is precisely 2. The summation of labels on the vertices of the graph which satisfy the PID labelling is known as its PID number, and is the minimum possible PID number of a graph G. We find some characterization of graphs for which . We also find a lower bound for |V(G)|, which satisfies the same. Further, we discuss the graphs that satisfies or . A realisation problem is used to prove that PID cannot be bounded by a scalar multiple of the Domination number. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024. -
On some classes of equitable irregular graphs
Graph labeling techniques are used by data scientists to represent data points and their relationships with each other. The segregation/sorting of similar datasets/points are easily done using labeling of vertices or edges in a graph. An equitable irregular edge labeling is a function $$f: E(G) \rightarrow N$$ (not necessarily be injective) such that the vertex sums of any two adjacent vertices of $$G$$ differ by at most one, where vertex sum of a vertex is the sum of the labels under $$f$$ of the edges incident with that vertex. A graph admitting an equitable irregular edge labeling is called an equitable irregular graph (EIG). In this paper, more classes of equitable irregular graphs are presented. We further generalize the concept of equitable irregular edge labeling to $$k$$-equitable irregular edge labeling by demanding the difference of the vertex sum of adjacent vertices to be $$k \ge 1$$. The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2021. -
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 near-perfect numbers with five prime factors
Let n be a positive integer and ?(n) the sum of all the positive divisors of n. We call n a near-perfect number with redundant divisor d if ?(n) = 2n + d. Let n be an odd near-perfect number of the form n = pa11 ? pa22 ? pa33 ? pa44 ? pa55 where pis are odd primes and ais (1 ? i ? 5) are positive integers. In this article, we prove that 3 | n and one of 5, 7, 11 | n. We also show that there exists no odd near-perfect number when n = 3a1 ? 7a2 ? pa33 ? pa44 ? pa55 with p3 ? {17, 19} and when n = 3a1 ? 11a2 ? pa33 ? pa44 ? pa55 Mathematical and Computational Sciences - Proceedings of the ICRTMPCS International Conference 2023.All rights reserved. -
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 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.