For any two vertices u and v in a graph G (digraph D, respectively), a u − v geodesic is a shortest path between u and v (from u to v, respectively). Let I(u, v) denote the set of all vertices lying on a u− v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) (g(D), respectively) of a graph G (digraph D, respectively) is the minimum ...

the basic National horizontal and vertical networks of geodetic control and provides governmentwide leadership in the improvement of geodetic surveying methods and instrumentation, coordinates operations to assure network development, and provides specifications and criteria for survey operations by Federal, State, and other agencies. NGS engages in research and development for the improvement ...

In our standard geodetic VLBI solutions, we estimate the positions of quasars assuming that their positions do not vary in time. However, in solutions estimating proper motion, a significant number of quasars show apparent proper motion greater than 50 μas/yr. For individual quasars, there are source structure effects that cause apparent proper motion. To examine how coherent the pattern of app...

Classic convexity can be extended to graphs in a natural way by considering shortest paths, also called geodesics: a set S of vertices of a graph is convex if it contains all the vertices lying in some geodesic with endpoints in S and the convex hull of a set S of vertices is the minimum convex set containing S. Farber and Jamison [9] characterized the graphs such that every convex set is the c...

A Steiner tree for a set S of vertices in a connected graph G is a connected subgraph of G with a smallest number of edges that contains S. The Steiner interval I (S) of S is the union of all the vertices of G that belong to some Steiner tree for S. If S = {u, v}, then I (S) = I [u, v] is called the interval between u and v and consists of all vertices that lie on some shortest u–v path in G. T...

the basic National horizontal and vertical networks of geodetic control and provides governmentwide leadership in the improvement of geodetic surveying methods and instrumentation, coordinates operations to ass ure network development, and provides specifications and criteria for survey operations by Federal, State, and other agencies. NGS engages in research and development for the improvement...