Department of Mathematics
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Item ANALYSIS OF UNEMPLOYMENT AMONG MOTHERS IN GOA(Education and Society, 2023) Almeida, MauriceItem On local distance antimagic labeling of graphs(AKCE International Journal of Graphs and Combinatorics, 2023) Godinho, AloysiusLet G = (V, E) be a graph of order n and let f : V → {1, 2 ... , n} be a bijection. For every vertex v ∈ V, we define the weight of the vertex v as w(v) = x∈N(v) f(x) where N(v) is the open neighborhood of the vertex v. The bijection f is said to be a local distance antimagic labeling of G if w(u) = w(v)for every pair of adjacent vertices u, v ∈ V. The local distance antimagic labeling f defines a proper vertex coloring of the graph G, where the vertex v is assigned the color w(v). We define the local distance antimagic chromatic number χld(G) to be the minimum number of colors taken over all colorings induced by local distance antimagic labelings of G. In this paper we obtain the local distance antimagic labelings for several families of graphs including the path Pn, the cycle Cn, the wheel graph Wn, friendship graph Fn, the corona product of graphs G ◦ Km, complete multipartite graph and some special types of the caterpillars. We also find upper bounds for the local distance antimagic chromatic number for these families of graphs.Item Distance antimagic labeling of join and corona of two graphs(/ AKCE International Journal of Graphs and Combinatorics 14 (2017) 172–177, 2017) Godinho, AloysiusItem Distance Antimagic Labeling of the Join & Corona Product of two Graphs(AKCE International Journal of Graphs and Combinatorics, 2017) Godinho, AloysiusLet G be a graph of order n. Let f∶ V (G)→{1, 2,..., n} be a bijection. The weight wf (v) of a vertex with respect to f is defined by wf (v)=∑ x∈ N (v) f (x). The labeling f is said to be distance antimagic if wf (u)≠ wf (v) for every pair of vertices u, v∈ V (G). If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we prove that Pm+ Pn, Pm+ Cn, Pm+ Wn and Cm+ Wn are distance antimagic. We have also proved that if G and H are distance antimagic graphs satisfying certain conditions, then G+ H is distance antimagic and if G is magic and H is arbirarily distance antimagic then G○ H is distance antimagic.Item Shear-thinning fluid flow in porous media: A study of boundary behavior using lattice Boltzmann method(International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 3, March 2017, pp. 13–21, 2017-03) Fernandes, IgnatiusSimulation of fluid flow in porous media using lattice Boltzmann method depends on how effectively collision, streaming and boundary conditions are implemented at micro level in view of the macroscopic behaviour of fluid. While collision and streaming have been extensively researched and attained effective formulation, boundary conditions still remains to be studied thoroughly. This paper studies various boundary conditions that are defined to simulate non-Newtonian fluid flow in porous media using lattice Boltzmann method. Further, these conditions are applied to simulate the problem of non-Newtonian forced convection in porous media and the variation in flow regimes and rate of heat transfer is studied based on the variation in velocity and thermal boundary behavior. Though velocity boundary conditions did not produce any difference in the flow regimes, thermal boundary conditions produced significant variation in rate of heat transferItem Group Distance Magic Labeling of Crn(Algorithms and Discrete Applied Mathematics, 2017) Godinho, AloysiusItem NUMERICAL SIMULATION OF FORCED CONVECTION IN OIL SANDS USING LATTICE BOLTZMANN METHOD(International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 78-89, 2016) Fernandes, IgnatiusLattice Boltzmann method is used to simulate forced convection in oil sands (low permeable porous geometries). Fluid flows through a sandstone look alike square geometry with left wall of the geometry kept at higher temperature compared to other walls. Investigation is carried out to study influence of increased temperature on flow properties by observing the variation in velocity and temperature profiles for various permeability and porosity values, which were varied to match the geometrical properties of oil sands. Boundary conditions and the relaxation parameter are suitably defined to achieve convergence for low values of permeability. Simulation was carried out at low Reynolds number, which however, can be extended to higher values of Reynolds number.Item Distance antimagic labeling of the ladder graph(Electronic Notes in Discrete Mathematics 63 (2017) 317–322, 2017) Godinho, AloysiusLet G be a graph of order n. Let f : V (G) −→ {1, 2,...,n} be a bijection. The weight wf (v) of a vertex with respect to f is defined by wf (v) = x∈N(v) f(x). The labeling f is said to be distance antimagic if wf (u) = wf (v) for every pair of vertices u, v ∈ V (G). If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we investigate the existence of distance antimagic labeling in the ladder graph Ln ∼= P2Pn.Item Numerical Simulation of Blood Flow with Sodium Alginate (SA) Nano Particles in Stenosed Human Arteries in the presence of Body Acceleration(International Journal of Mechanical Engineering and Technology Volume 10, Issue 06, June 2019, 2019) Fernandes, IgnatiusNumerical simulation of blood flow with sodium alginate nano particles in stenosed human arteries in the presence of body acceleration is obtained. Effect of sodium alginate (SA) nano particles in the presence of body acceleration is observed on velocity, flow rate and resistive impedance to blood flow in stenosed human artery. The governing equations are discretized by explicit finite difference scheme. The discretized equations are the simulated using MATLAB. Velocity, flow rate and impedance to flow are observed to be influenced in the presence of both nano particles as well as body acceleration. The joint effect of nano particles and body acceleration is also observed. Resistance to flow is observed to be less in the presence of nano particles. This nano particle drug delivery may be useful for patients having cardiovascular diseases.Item Simulation of Natural Convection in Blood Flow using Lattice Boltzmann Method(Advances and Applications in Fluid Mechanics Volume 23, Number 1, 2019, Pages 25-44, 2019) Fernandes, IgnatiusLattice Boltzmann method is used to simulate natural convection in blood flow through stenotic artery. The problem of natural convection in stenotic artery is considered and the influence of elevated temperature and material properties is studied on the flow properties. A porous like square stenotic medium in a human artery with fluid (blood) at the left wall of the geometry and the north wall kept to a normalized temperature of 1.0 is considered. The flow properties like velocity profiles, streamlines, temperature profiles and the rate of heat transfer are then studied with respect to the material properties like porosity and permeability and flow parameters like Rayleigh number and power law index.Item Simulation of forced convection in non-Newtonian fluid through sandstones(International Journal for Computational Methods in Engineering Science and Mechanics Volume 18, 2017 - Issue 6, 2017-09) Fernandes, IgnatiusNumerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through sandstones. Simulation is carried out using lattice Boltzmann method (LBM) for both shear-thinning and shear-thickening, by varying the power law index from 0.5 to 1.5 in Carreau–Yasuda model. Parameters involved in LBM and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10−10–10−6 and 0.1–0.7, respectively, to match actual geometrical properties of sandstone. Numerical technology is validated by establishing Darcy's law by plotting the graph between velocity and pressure gradient. Consequently, investigation is carried out to study the influence of material properties of porous media on flow properties such as velocity profiles, temperature profiles, and Nusselt number.Item THE DISTANCE MAGIC INDEX OF A GRAPH(Discussiones Mathematicae Graph Theory 38 (2018) 135–142, 2018) Godinho, AloysiusLet G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection φ : V (G) → S satisfying P x∈N(u) φ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeling. Then i(G) − n is called the distance magic index of the graph G. In this paper we determine the distance magic index of trees and complete bipartite graphs.Item Some distance magic graphs(AKCE International Journal of Graphs and Combinatorics 15 (2018) 1–6, 2018) Godinho, AloysiusA graph G = (V, E), where |V| = n and |E| = m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set {1, 2, . . . , n} such that, ∑ v∈N(u) f (v) = k, for all u ∈ V, which is a constant and independent of u, where N(u) is the open neighborhood of the vertex u. The constant k is called the distance magic constant of the graph G and such a labeling f is called distance magic labeling of G. In this paper, we present new results on distance magic labeling of C r n and neighborhood expansion Dn(G) of a graph G.Item Lattice Boltzmann Simulation of Forced Convection in Non-Newtonian Fluid Through Low Permeable Porous Media(Far East Journal of Mathematical Sciences Volume 100, Number 2, 2016, Pages 315-332, 2016-07) Fernandes, IgnatiusNumerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through low permeable porous media like sandstones and sand. Simulation is carried out using lattice Boltzmann method for both shear-thinning and shear-thickening, by varying the power-law index from 0.5 to 1.5 in Carreau-Yasuda model. Parameters involved in lattice Boltzmann method and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10 10Item On nearly distance magic graphs(International Conference, ICTCSDM 2016, Krishnankoil, India, December 19-21, 2016, 2017) Godinho, AloysiusLet G = (V, E) be a graph on n vertices. A bijection f ∶ V → {1, 2, . . . , n} is called a nearly distance magic labeling of G if there exist a positive integer k such that ∑x∈N(v) f(x) = k or k +1 for every v ∈ V . The constant k is called magic constants of the graph and the graph which admits such a labeling is called a nearly distance magic graph. In this paper we present several basic results on nearly distance magic graphs and compute the magic constant k in terms of the fractional total domination number of the graph.Item Reconstruction of hypergraphs from line graphs and degree sequences(arXiv:2104.14863v1, 2021) Godinho, AloysiusIn this paper we consider the problem to reconstruct a k-uniform hypergraph from its line graph. In general this problem is hard. We solve this problem when the number of hyperedges containing any pair of vertices is bounded. Given an integer sequence, constructing a k-uniform hypergraph with that as its degree sequence is NP-complete. Here we show that for constant integer sequences the question can be answered in polynomial time using Baranyai’s theorem.Item Some distance antimagic labeled graphs(Algorithms and Discrete Applied Mathematics (pp. 190-200)., 2016-02) Godinho, AloysiusLet G be a graph of order n. A bijection f : V (G) −→ {1, 2, . . . , n} is said to be distance antimagic if for every vertex v the vertex weight defined by wf (v) = P x∈N(v) f(x) is distinct. The graph which admits such a labeling is called a distance antimagic graph. For a positive integer k, define fk : V (G) −→ {1 + k, 2 + k, . . . , n + k} by fk(x) = f(x) + k. If wfk (u) 6= wfk (v) for every pair of vertices u, v ∈ V , for any k ≥ 0 then f is said to be an arbitrarily distance antimagic labeling and the graph which admits such a labeling is said to be an arbitrarily distance antimagic graph. In this paper, we provide arbitrarily distance antimagic labelings for rPn, generalised Petersen graph P(n, k), n ≥ 5, Harary graph H4,n for n 6= 6 and also prove that join of these graphs is distance antimagic.