Given a simple connected graph G = (V, E) the geodetic closure I[S] ⊂ V of a subset S of V is the union of all sets of nodes lying on some geodesic (or shortest path) joining a pair of nodes vk, vl ∈ S. The geodetic number, denoted by g(G), is the smallest cardinality of a node set S∗ such that I[S∗] = V . In “The geodetic number of a graph”, Mathematical and Computer Modelling 17 (June 1993) 8...

This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a result, the enumeration of the class of geodetic graphs homeomorphic to certain Moore graphs has been performed.

For two vertices u and v of a connected graph G, the set IG[u, v] consists of all those vertices lying on u − v geodesics in G. Given a set S of vertices of G, the union of all sets IG[u, v] for u, v ∈ S is denoted by IG[S]. A set S ⊆ V (G) is a geodetic set if IG[S] = V (G) and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong ...

Modern geodetic observations from a wide range of space and terrestrial technologies contribute to our knowledge of the solid Earth, atmosphere, ocean, cryosphere, and land water storage. These geodetic observations record the “fingerprints” of global change processes and thus are a crucial independent source of high accuracy information for many global change studies. Many of the geodetic tech...

With the availability of low-cost, mass-market dual-frequency GNSS (Global Navigation Satellite System) receivers, standalone processing methods such as Precise Point Positioning (PPP) are no longer restricted to geodetic-grade equipment only. However, with cheaper equipment, data quality is expected degrade. This same principle also affects low-cost antennas, which usually suffer from poorer m...

Academia, Industry and Government are investigating the reliability to use the real time kinematic (RTK) Global Navigation Satellite System (GNSS) techniques for centimetre level positioning of many existing and emerging applications. These include for instance mobile mapping and airborne laser scanning systems. The classical RTK methodology allows for an operational distance between the refere...

Geodetic velocity (GV) has many applications in tectonic motion determination and geodynamic studies. Due to the high cost of global navigation satellite system stations, deep learning methods have been investigated estimate GV. In this research, four convolutional neural networks (CNNs), Boltzmann machines, belief net recurrent applied. The GV 42 positioning stations is entered methods. output...

The occurrence of cycle slips is a major limiting factor for achievement of sub-decimeter accuracy in positioning with GPS (Global Positioning System). In the past, several authors introduced a method based on different combinations of GPS data together with Kalman filter to solve the problem of the cycle slips. In this paper the same philosophy is used but with discrete wavelet transforms. For...

Abstract In this study, positioning quality is tested with the use of low-cost in-house developed receivers. The analyzes consider practical devices in surveying works. network solution, accuracy GNSS based on receivers can be characterized by repeatability baseline length 1 and 6 mm 24 h 10 min observation sessions, respectively. field experiment 4 3 allowed for establishing a precise geodetic...