For a connected graph G of order n, a set S ⊆ V (G) is a geodetic set of G if each vertex v ∈ V (G) lies on a x-y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set of G is defined as the geodetic number of G, denoted by g(G). A geodetic set of cardinality g(G) is called a g-set of G. A set S of vertices of a connected graph G is an open geodetic set of G if for ...

For a connected graph G = (V,E), a set S ⊆ E is called an edge-to-vertex geodetic set of G if every vertex of G is either incident with an edge of S or lies on a geodesic joining some pair of edges of S. The minimum cardinality of an edge-to-vertex geodetic set of G is gev(G). Any edge-to-vertex geodetic set of cardinality gev(G) is called an edge-to-vertex geodetic basis of G. A subset T ⊆ S i...

Geocentric translation model (GTM) in recent times has not gained much popularity in coordinate transformation research due to its attainable accuracy. Accurate transformation of coordinate is a major goal and essential procedure for the solution of a number of important geodetic problems. Therefore, motivated by the successful application of Artificial Intelligence techniques in geodesy, this ...

Efficient transformation parameters are key to effective geodetic operations between any systems. With the advancement in technology, an improved interaction reference frames has been noticed irrespective of their inherent heterogeneous deformations and intermittently present oversight that exist as a result conversion methodology. The spatial data captured using Global Navigation Satellite Sys...

Difference representations on curvilinear coordinate systems are constructed by first transforming derivatives with respect to cartesian coordinates into expressions involving derivatives with respect to the curvilinear coordinates (the metric coefficients). The derivatives with respect to the curvilinear coordinates are then replaced with difference expressions on the uniform grid in the trans...

In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only with the velocity but also with the str...

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.), as well as rapidly-evolving systems. The technique employed is the Finite Element Method (FEM), which has been used to solve engineering struc...