• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.155-163
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• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.525-532
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• 2004

For two vertices u and v of an oriented graph D, the set I(u, v) consists of all vertices lying on a u-v geodesic or v-u geodesic in D. If S is a set of vertices of D, then I(S) is the union of all sets 1(u, v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the subsets S of V(D) with I(S) = V(D). In this paper, we give a partial answer for the conjecture by G. Chartrand and P. Zhang and present some results on orient able geodetic number.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.503-509
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• 2014

For a connected graph G, there are orientations of G have different hull numbers, geodetic numbers, and convexity numbers. The lower orientable hull number $h^-(G)$ is defined as the minimum hull number among all the orientations of G and the upper orientable hull number $h^+(G)$ as the maximum hull number among all the orientations of G. The lower and upper orientable geodetic numbers $g^-(G)$ and $g^+(G)$ are defined similarily. In this paper, We investigate characterizations of the orientable numbers and the conditions that the relation $h^-(G){\leq}g^-(G)$ < $h^+(G){\leq}g^+(G)$ holds.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.255-266
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• 2014

For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.29 no.4
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• pp.367-380
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• 2011

This paper has focused on deriving a GPS based geodetic network adjustment strategy to continuously determine coordinate sets of the national geodetic control points. After domestic literature review on the topic and overseas case studies about countries that recently reformed their geodetic infrastructure have been carried out, a simplified geodetic network consisting of two layers, namely GPS active and passive network, has been proposed to maximize effectiveness of the network adjustment through reducing the number of the passive points. Furthermore, a GPS data processing and network adjustment procedure has been derived to support the continuous management scheme. While a scheme for the active layer adopts a sequential least squares adjustment based on a multi-baseline, that of the passive layer employs a multi-session adjustment technique with respect to 3-dimensional baseline vectors. Finally, experimental adjustment against a network comprising 24 active and 6,900 passive stations has been performed to demonstrate the efficiency and the effectiveness of the proposed method.

• Computers and Concrete
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• v.20 no.1
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• pp.23-29
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• 2017

In this study engineered steel fibres used as reinforcement for concrete were characterized by number of key mechanical and spatial parameters, which are easy to measure and quantify. Such commonly used parameters as length, diameter, fibre intrinsic efficiency ratio (FIER), hook geometry, tensile strength and ductility were considered. Effective classification of various fibres was demonstrated using simple multivariate computations involving principal component analysis (PCA). Contrary to univariate data mining approach, the proposed analysis can be efficiently adapted for fast, robust and direct classification of engineered steel fibres. The results have revealed that in case of particular spatial/geometrical conditions of steel fibres investigated the FIER parameter can be efficiently replaced by a simple aspect ratio. There is also a need of finding new parameters describing properties of steel fibre more precisely.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.1
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• pp.677-682
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• 2009

According to the revised law of survey, all the geographic information data including 1/1,000 digital topographic maps have to be converted to world geodetic reference system by the end of 2009. National Geographic Information Institute (NGII) formulated the policy to promote the conversion from local geodetic reference system to world geodetic reference system. However, the current conversion rate is lower than planned due to some impeding factors. Therefore, in this paper, those impeding factors are investigated and then efficient conversion strategies are established and provided. The research involves the validation of affine transformation, the determination of critical value for outlier detection and optimal number of common control points for coordinate conversion, and the treatment of old and new control points.

• Structural Monitoring and Maintenance
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• v.8 no.4
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• pp.309-328
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• 2021

The objective of this work was to develop a methodology for geodetic monitoring on onshore wind towers, to ascertain the existence of displacements from object points located in the tower and at the foundation's base. The geodesic auscultation was carried out in the Gravatá 01 and 02 wind towers of the Eólica Gravatá wind farm, located in the Brazilian municipality of Gravatá-PE, using a stable Measurement Reference System. To verify the existence of displacements, pins were implanted, with semi-spherical surfaces, at the bases of the towers being monitored, measured by means of high-precision geometric leveling and around the Gravatá 02 tower, concrete landmarks, iron rods and reflective sheets were implanted, observed using geodetic/topographic methods: GNSS survey, transverse with forced centering, three-dimensional irradiation, edge measurement method and trigonometric leveling of unilateral views. It was found that in the Gravatá 02 tower the average rays of the circular sections of the transverse welds (ST) were 1.8431 m ± 0.0005 m (ST01) and 1.6994 m ± 0.0268 m of ST22, where, 01 and 22 represent the serial number of the transverse welds along the tower. The average calculation of the deflection between the coordinates of the center of the circular section of the ST22 and the vertical reference alignment of the ST1 was 0°2'39.22" ± 2.83" in the Northwest direction and an average linear difference of 0.0878 m ± 0.0078 m. The top deflection angle was 0°8'44.88" and a linear difference of ± 0.2590 m, defined from a non-linear function adjusted by Least Squares Method (LSM).

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.805-810
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• 2017

Let $C_n$ be the cycle graph of order n on the vertices $v_0,v_1,{\ldots},v_n$ and $C^k_n$ be the k-th power of $C_n$. In this article we determine the hull-number of $C^k_n$.