For two vertices u and v of a graph G, the closed interval I[u, v] consists of u, v, and all vertices lying in some u − v geodesic in G. If S is a set of vertices of G, then I[S] is the union of all sets I[u, v] for u, v ∈ S. If I[S] = V (G), then S is a geodetic set for G. The geodetic number g(G) is the minimum cardinality of a geodetic set. A set S of vertices in a graph G is uniform if the ...

For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u − v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u, v) for u, v ∈ S. A set S is a geodetic set if I(S) = V (G). A minimum geodetic set is a geodetic set of minimum cardinality and this cardinality is the geodetic number g(G). A subset T of a minimum geodetic set...

This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Gal...

We present a rupture model of the Northridge earthquake, determined from the joint inversion of near-source strong ground motion recordings, P and SH teleseismic body waves, Global Positioning System (GPS) displacement vectors, and permanent uplift measured along leveling lines. The fault is defined to strike 122 ° and dip 40 ° to the south-southwest. The average rake vector is determined to be...

The idea of constructing the “GNSS-like” seafloor geodetic network for underwater positioning, navigation, and timing (PNT) has been proposed by many countries. Based on this idea, paper introduces principle PNT provides a combined measurement method, including absolute positioning relative positioning. Experimental results show that difference between method circle-sailing is approximately 10 ...

With the gravity eld and steady-state ocean circulation explorer (GOCE) (preferably combined with the gravity eld and climate experiment (GRACE)) a new generation of geoid models will become available for use in height determination. These models will be globally consistent, accurate (<3 cm) and with a spatial resolution up to degree and order 200, when expressed in terms of a spherical harmoni...

The accuracy of current modern space-based geodetic systems such as Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), the Global Positioning System (GPS), and satellite altimetry all suffer from limitations in the modeling of atmospheric refraction corrections. The current modeling of atmospheric refraction in the analysis of SLR data comprises the determination of the at...

-Given two vertices u and v of a connected graph G=(V, E), the closed interval I[u, v] is that set of all vertices lying in some u-v geodesic in G. A subset of V(G) S={v1,v2,v3,....,vk} is a linear geodetic set or sequential geodetic set if each vertex x of G lies on a vi – vi+1 geodesic where 1 ≤ i < k . A linear geodetic set of minimum cardinality in G is called as linear geodetic number lgn(...

A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimum cardinality of a geodetic set of G. We prove that it is NP complete to decide for a given chordal or chordal bipartite graph G and a given integer k whether G has a geodetic set of cardinality at most k. Furthermore...

A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D. A geodetic dominating set S is both a geodetic and a dominating set. The geodetic (domination, geodetic domination) number g(G)(γ(G), γg(G)) of G is...