In the integration of geodetic networks with different geodetic coordinate systems, the similarity transformation seems to be the most suitable method because the geodetic coordinate systems are designated to be Cartesian (orthogonal). However, this method may always not be practical to use in most surveying works demanding such high accuracies as the coordinates used in the transformation are ...

Let G : (V, E, ω) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function ω: E    . A u−v path P in G is called a weighted u−v geodesic if the weighted distance between u and v is calculated along P. The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in...

Let k ≥ 2 be an integer, a k-decomposition (G1,G2, . . . ,Gk) of the complete graph Kn is a partition of its edge set to form k spanning subgraphs G1,G2, . . . ,Gk. In this contribution, we investigate the Nordhaus–Gaddum-type inequality of a k-decomposition of Kn for the general Zagreb index and a 2-decomposition for the Zagreb co-indices, respectively. The corresponding extremal graphs are ch...

A decomposition of a graph is a partition of the edge set, giving a set of subgraphs. A transitive decomposition is a decomposition which is highly symmetrical, in the sense that the subgraphs are preserved and transitively permuted by a group of automorphisms of the graph. This paper describes some ‘product’ constructions for transitive decompositions of graphs, and shows how these may be used...

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic of cardinality dg(G) is called dg-set of G. The double geodetic numbers of certain standard graphs are o...

[1] The geodetic velocity and strain rate patterns in Anatolia constrain the rheology of the lithosphere, once compared with thin shell finite element tectonic model predictions. Geodetic and modeled deformation favors a hard lithospheric rheology, responsible for the high EastWest horizontal velocities in the center of Anatolia, between 39 –41 N, in proximity of the North Anatolian Fault. The ...

Let tt : (V, E, W ) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function W : E +. A u v path P in tt is called a weighted u v geodesic if the weighted distance between u and v is calculated along P . The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in...

We give a complete solution to the existence problem for complementary P3-decompositions of the complete multigraph, where P 3 denotes the path of length 3. A complementary decomposition 2>.K v (P 3 , P 3) is an edge decomposition of the complete multigraph >'Kv into P 3 '8 with the property that upon taking the complement of each path one obtains a second decomposition of >'K3 into P3 '8 (wher...

A brief Note compiled by: Prof. Madhav N. Kulkarni, IIT Bombay Since the inception of the Very Long Baseline Interferometry (VLBI) system in 1967, this radio interferometry technique has revolutionised the fields of geodesy, geodynamics and astrometry. With the unprecedented precision and resolution made possible by VLBI various tasks such as geodetic positioning, reference frames interconnect...

Let G be an undirected bipartite graph with positive integer weights on the edges. We refine the existing decomposition theorem originally proposed by Kao et al., for computing maximum weight bipartite matching. We apply it to design an efficient version of the decomposition algorithm to compute the weight of a maximum weight bipartite matching of G in O( √ |V |W ′/k(|V |,W ′/N))-time by employ...