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a-Domination of Cartesian Product of Path Semigraphs
In a scientific enquiry it is common to study the behaviour of combined systems after studying the systems individually. The graphical structures are combined in many ways. The Cartesian product is one of the way of combining graphs to get more general structures from the simple structures. In this paper, we study a-domination number of the Cartesian product of some simple path semigraphs.
Journal Article
Interval vertex coloring of cartesian products and strong products of paths
For the graph’s vertex coloring, it is required that for every vertex in a graph, the colors used in its open neighborhood or closed neighborhood must be able to form a continuous integer interval. A coloring is called an open neighborhood interval vertex coloring or a closed neighborhood interval vertex coloring of a graph if the neighborhood satisfying the condition is open or closed. In this paper, the interval vertex coloring of cartesian products and strong products of two paths is studied, and the low bound of the interval chromatic number is given.
Journal Article
The Cartesian background: England and France
The 17th and 18th century opposition between Cartesian and Newtonian science is often depicted as a contest between a priorism and speculation on one hand, and observation and mathematical proof on the other, one of which won out. This is a simplification. In 17th century England Cartesian natural philosophy, including the vortex theory of the planetary orbits, was (intentionally) easy to understand. It was seen however as poorly disguised atheism and widely disparaged on that account by influential theologians. Amongst the 18th century French philosophes, this aspect of Cartesianism was hardly a problem. Newtonianism now denoted an appetite for exciting experimental demonstrations as against the dead letter of scientific books, including not only René Descartes’s Principles but also Isaac Newton’s (for most readers) largely impenetrable Principia .
Journal Article
On cubic non-linearities in fluid and kinetic models
The kinetic origin of the cubic terms found in electromagnetic reduced fluid models of magnetized plasmas is identified and analyzed. The transition from cartesian to guiding center variables in kinetic systems is responsible for the introduction of such cubic terms, and the derivation of a set of such terms is explicitly shown. The role of these terms in fluid simulations, and their importance for energy conservation of cubic terms in both frameworks is discussed
Journal Article
Graph Theoretic Insights into Corona Domination and Cartesian Products
In this article we provide a contribution to study the corona domination number( CD -number) for the Cartesian product of graphs. A dominating set S of a graph H is said to be a corona dominating set ( CD – set ) if every vertex in ⟨ S ⟩ is either a pendant vertex or a support vertex. The minimum cardinality of a corona dominating set is called the corona domination number and is denoted by γ CD ( H ). Also the characterization of Cartesian product of some graphs in terms of this parameter were discussed and the exact γ CD value for the graphs consider in the article are identified using some number theory technique.
Journal Article
Product of bipolar anti fuzzy graph and their degree of vertex
Based on complete bipolar anti fuzzy graphs and on strong bipolar anti fuzzy graphs we can define a new graph through union, join, Cartesian product, and composition of such two graphs. We call the new graph as a product of graphs. In this article we investigate properties of product of bipolar anti fuzzy graphs and product of strong bipolar anti fuzzy graphs. We also construct the degree of a vertex in such the product, namely, the degree of a vertex in the graph which are obtained from product of two given bipolar anti fuzzy graph.
Journal Article
1e-Domination on Cartesian Product of Path Semigraphs
Semigraphs are the more general form of graphs. The graphical structure of semigraphs are combined in several ways. The Cartesian product is one of the way of combining graphs to get more general structures from the simple structure of graphs. In this paper, 1e-domination number of the Cartesian product of some simple path semigraphs are discussed.
Journal Article
A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering
The formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as accurate as existing nonhydrostatic solvers for nonhydrostatic-scale flows, and has accuracy comparable to existing global models using icosahedral (hexagonal) meshes for large-scale flows in idealized tests. Preliminary full-physics forecast results indicate that the solver formulation is robust and that the variable-resolution-mesh solutions are well resolved and exhibit no obvious problems in the mesh-transition zones.
Journal Article
THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES
The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.
Journal Article