This article describes currently used analysis strategy and data analysis software for geodetic VLBI. Today’s geodetic observing strategies are shortly presented, and the geodetic VLBI observables and data modeling are briefly discussed. A short overview is given on existing geodetic VLBI software packages and the statistical approaches that are applied. Necessary improvements of today’s analys...

A subset S of vertices in a graph G is a called a geodetic dominating set if S is both a geodetic set and a (standard) dominating set. In this paper, we study geodetic domination on graphs.

Since the definition of the Geocentric Datum of Australia in 1994 (GDA94), Australia has had a GPS continuously operating reference station (CORS) network for datum maintenance. The Australian Fiducial Network (AFN) now comprises eight geologically stable, geodetic quality GNSS CORS stations which also contribute to the Australian Regional Geodetic Network and the International GNSS Network. In...

Introducing certain types of morphisms for general (abstract) convexity spaces, we give several ways for reducing the (Calder-) Eckhoff partition problem to simpler equivalent forms (finite, point-convex, interval spaces; restricted form, i.e. with distinct points). With additional results (to appear in a forthcoming paper) we show how the general problem can be reduced to its restricted versio...

We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call " geodetic ". We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecom...

The geodetic problem was introduced by Harary et al. [17]. In order to model some social network problems, a similar problem is introduced in this paper and named the strong geodetic problem. The problem is solved for complete Apollonian networks. It is also proved that in general the strong geodetic problem is NP-complete.

An undirected graph G = (V;E) is said to be geodetic, if between any pair of vertices x; y 2 V there is a unique shortest path. Generalizations of geodetic graphs are introduced in this paper. K-geodetic graphs are de ned as graphs in which every pair of vertices has at most k paths of minimum length between them. Some properties and characterizations of k{geodetic graphs are studied.

In the paper four semirings for solving social networks problems are constructed. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable. The closure of relational matrix over geodetic semiring contains for every pair of vertices and the length and the number of geodesics; and for geosetic semiring...

We give a linear-time algorithm for computing the edge search number of cographs, thereby resolving the computational complexity of edge searching on this graph class. To achieve this we give a characterization of the edge search number of the join of two graphs. With our result, the knowledge on graph searching of cographs is now complete: node, mixed, and edge search numbers of cographs can a...