Let G be an undirected graph with vertex and edge sets V (G) E(G), respectively. A subset S of vertices is a geodetic hop dominating set if it both set. The domination number G, γhg(G), the minimum cardinality among all in G. Geodetic resulting from some binary operations have been characterized. These characterizations used to determine tight bounds for each graphs considered.

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...

A set U of vertices of a graph G is called a geodetic set if the union of all the geodesics joining pairs of points of U is the whole graph G. One result in this paper is a tight lower bound on the minimum number of vertices in a geodetic set. In order to obtain that result, the following extremal set problem is solved. Find the minimum cardinality of a collection S of subsets of 1⁄2n 1⁄4 f1; 2...

The Radon number of a graph is the minimum integer r such that all sets of at least r vertices of the graph can be partitioned into two subsets whose convex hulls intersect. We present a near-linear O(d log d) time algorithm to calculate the Radon number of d-dimensional grids in the geodetic convexity. To date, no polynomial time algorithm was known for this problem.

Abstract: The availability of GLONASS would bring significant benefits to geodetic applications of global positioning systems. GPS and GLONASS observations could be combined directly in the data processing; as a result, the geometry of observed satellites could be enhanced by increasing the number of available satellites. Up to now, with the recent revitalization of GLONASS, more high precision...

A “dynamic” geodetic datum is a datum that consists of coordinates and velocities of control points, which can provide users with the realistic positions of sites within the network that reflects the result of local or regional motion induced by a number of causes. A new ITRF-linked scheme is proposed and discussed in order to process available geodetic data in real-time to establish a dynamic ...

[1] We have applied a thin-shell modeling technique to study the neotectonics of the Caribbean plate. Kinematic conditions computed assuming rotation poles and velocities from NUVEL-1A and from recent geodetic studies have been applied at the lateral boundaries of the model to represent the motion of the adjacent plates with respect to the Caribbean. We have generated a large number of models v...

Due to the limited resolution at depth of geodetic and other geophysical data, the geometry and the loading rate of the ramp-décollement faults below the metropolitan Los Angeles are poorly understood. Here we complement these data by assuming conservation of motion across the Big Bend of the San Andreas Fault. Using a Bayesian approach, we constrain the geometry of the ramp-décollement system ...

The edge C4 graph of a graph G, E4(G) is a graph whose vertices are the edges of G and two vertices in E4(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C4. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C4 graphs are isomorphic. We study the relationship between the diameter, radius and domina...

Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if there exists a vertex u such that no neighbor of v is further away from u than v. We obtain a number of properties involving different types of boundary vertices: peripheral, contour and eccentric vertices. Before showing that one of the main results in [3] does not hold for one of the cases, we establish a realiz...