• Korean Journal of Mathematics
• /
• v.18 no.4
• /
• pp.369-380
• /
• 2010

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.22 no.11
• /
• pp.1538-1543
• /
• 2018

For n pairs of points (a,b) on a circle, the line segment to connect two points is called a chord. These chords define a new graph G. Each chord corresponds to a vertex of G, and if two chords intersect, the two vertices corresponding to them are connected by an edge. This makes a graph, called by a circle graph. In this paper, we deal with the problem to find the connected components of a circle graph. The connected component of a graph G is a maximal subgraph H such that any two vertices in H can be connected by a path. When the adjacent matrix of G is given, the problem to find them can be solved by either the depth-first search or the breadth-first search. But when only the information for the chords is given as an input, it takes ${\Omega}(n^2)$ time to obtain the adjacent matrix. In this paper, we do not make the adjacent matrix and develop an $O(n{\log}^2n)$ algorithm for the problem.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1433-1443
• /
• 2015

Catenoid and Riemann's minimal surface are foliated by circles, that is, they are union of circles. In $\mathbb{R}^3$, there is no other nonplanar example of circle-foliated minimal surfaces. In $\mathbb{R}^4$, the graph $G_c$ of w = c/z for real constant c and ${\zeta}{\in}\mathbb{C}{\backslash}\{0}$ is also foliated by circles. In this paper, we show that every circle-foliated minimal surface in $\mathbb{R}$ is either a catenoid or Riemann's minimal surface in some 3-dimensional Affine subspace or a graph surface $G_c$ in some 4-dimensional Affine subspace. We use the property that $G_c$ is circle-foliated to construct circle-foliated minimal surfaces in $S^4$ and $H^4$.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2000.05a
• /
• pp.739-742
• /
• 2000

From the experimental study of W-EDM for alloyed steel, the characteristics such as Hand Drum Form and surface roughness have been observed and evaluated for various conditions. In square hole, the increase of If as to made condition the calculate high value of surface roughness. Also compare dimensionless square hole with circle hole' graph. In circle hole, if a value of surface roughness IP 6 in a side of circle it show a 0.4${\mu}{\textrm}{m}$ and in IP 8, 0.6${\mu}{\textrm}{m}$, in IP 10, 0.7${\mu}{\textrm}{m}$, in IP 12. 0.8${\mu}{\textrm}{m}$ higher than before. This figure show the surface roughness is higher than before, because a table move in either X-axis or Y-axis in square hole, on the contrary, in circle there table move in X-axis and Y-axis at the same time. hand drum form getting small when wire tension increase 1000gf to 1500gf, at the same working conditions. the smaller of off time, the mailer of hand drum form in same condition and same wire tension. but if you compare square hole with circle hole' graph hand drum form displayed in maintained term of working condision, on the contrary, in case of square hole variation of hand drum form is more increase than a grow of IP

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 2000.04a
• /
• pp.567-572
• /
• 2000

From the experimental study of W-EDM for alloyed steel, the characteristics such as Hand Drum Form and surface roughness have been observed and evaluated for various conditions. In square hole, the increase of IP as to made condition, the calculate high value of surface roughness. Also compare dimensionless square hole with circle hole' graph, In circle hole, if a value of surface roughness IP 6 in a side of circle it show a 0.4${\mu}{\textrm}{m}$ and in IP 8, 0.6${\mu}{\textrm}{m}$, in IP 10, 0.7${\mu}{\textrm}{m}$, in IP 12, 0.8${\mu}{\textrm}{m}$ higher than before. This figure show the surface roughness is higher than before, because a table move in either X-axis or Y-axis in square hole, on the contrary, in circle there table move in X-axis and Y-axis at the same time. hand drum form getting small when wire tension increase 1000gf to 1500gf, at the same working conditions. The smaller of off time, the maller of hand drum form in same condition and same wire tension. but if you compare square hole with circle hole' graph, hand drum form displayed in maintained term of working condision, on the contrary, in case of square hole variation of hand drum form is more increase than a grow of IP

• School Mathematics
• /
• v.1 no.2
• /
• pp.555-569
• /
• 1999

The graph unit(chapter) is a good example of a topic in elementary school mathematics for which computer use can be incorporated as part of the instruction. Teaching graph can be facilitated by using the graphing utilities of computers, which make it possible to observe the property of many types of graphs. This study was concerned with utilizing an educational software Graphers as an instructional tool in teaching to help young students gain a better understanding of graph concepts. For this purpose, three types of instructional activities using Graphers were shown in the paper. Graphers is a data-gathering tool for creating pictorial data chosen from several data sets. They can represent their data on a table or with six types of graphs such as Pictograph, Bar Graph, Line Graph, Circle Graph, Grid Plot and Loops. They help students to select the graph(s) which are the most appropriate for the purpose of analyzing data while comparing various types of graphs. They also let them modify or change graphs, such as adding grid lines, changing the axis scale, or adding title and labels. Eventually, students have a chance to interpret graphs meaningfully and in their own way.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2011.11a
• /
• pp.1166-1169
• /
• 2011

In this paper, we design a Circle dot Code, In our scheme, we design a dot patterns for increasing maximum capacity and also for increasing robustness to Affine Transformation. Our code Can be extended according number of data circle. We use three data circle vision code. In this type code, after acquiring camera images for the Circle dot Codes, and perform error correction decoding using four position symbols and six CRC symbols. We perform graph based dot code analysis which determines the topological distance between dot pixels. Our code can be bridged the real world and ubiquitous computing environment.

• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.227-248
• /
• 2017

In this paper, we reduce the classification problem of equivariant (topological complex) vector bundles over a simple graph to the classification problem of their isotropy representations at vertices and midpoints of edges. Then, we solve the reduced problem in the case when the simple graph is homeomorphic to a circle. So, the paper could be considered as a generalization of [3].

• Journal of the Korean Operations Research and Management Science Society
• /
• v.27 no.4
• /
• pp.1-10
• /
• 2002

The ring routing and wavelength assignment problem arose in the planning of optical communication networks which use WDM rings. Traffic demands are given for each pair of nodes in an ring : each demand must be routed one of the two possible connections round the ring and the wavelength assignments must be made so that there are no conflicts : that is. no two connections whose routes share a link can be assigned the same wavelength along that link. The objective is to minimize the number of used wavelengths. We propose the local optimal routing for the problem and show that there always exists an optimal solution satisfying it. Furthermore we suggest a new lower bound for the problem and show that it is very efficient for the worst case example.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.21 no.11
• /
• pp.2103-2108
• /
• 2017

For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.