We show that for every integer k ≥ 2 and every k graphs G1, G2, . . . , Gk, there exists a hull graph with k hull vertices v1, v2, . . . , vk such that link L(vi) = Gi for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a, b of integers with a ≥ 2 and b ≥...

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...

Due to the relative lack of empirical field data, the response of very small glaciers (here defined as being smaller than 0.5 km2) to current atmospheric warming is not fully understood yet. Investigating their mass balance, e.g. using the direct glaciological method, is a prerequisite to fill this knowledge gap. Terrestrial laser scanning (TLS) techniques operating in the near infrared range c...

Abstract Metsähovi Geodetic Research Station (MGRS) of the National Land Survey Finland, has undergone a major upgrade. The first observations at MGRS were started in 1978. A decade-long reform began 2012, during which all systems renewed. This included Global Navigation Satellite System (GNSS) station, Laser Ranging (SLR) system, and dedicated geodetic Very Long Baseline Interferometer (VLBI) ...

Abstract The article gives an overview of the structural elements geodetic networks various types. For satellite networks, a promising method using mobile monitoring and control stations is considered. This provides increase in reliability stability orbital constellation, however, when implementing it, it necessary to pay special attention issue referencing antennas stations. problem support fo...

We show that the geodetic number of proper interval graphs can be computed in polynomial time. This problem is NP-hard on chordal graphs and on bipartite weakly chordal graphs. Only an upper bound on the geodetic number of proper interval graphs has been known prior to

Due to the relative lack of empirical field data, the response of very small glaciers (<0.5 km) to current atmospheric warming is not fully understood yet. Investigating their mass balance is a prerequisite to fill this knowledge gap. Application of the direct glaciological method is one option. Since most recently, terrestrial laser scanning (TLS) techniques operating in the near infrared rang...