• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.595-608
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• 2013

Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.1
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• pp.33-45
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• 2011

In this paper, we present a method for extracting video objects efficiently by using the modified graph cut algorithm based on contour information. First, we extract objects at the first frame by an automatic object extraction algorithm or the user interaction. To estimate the objects' contours at the current frame, motion information of objects' contour in the previous frame is analyzed. Block-based histogram back-projection is conducted along the estimated contour point. Each color model of objects and background can be generated from back-projection images. The probabilities of links between neighboring pixels are decided by the logarithmic based distance transform map obtained from the estimated contour image. Energy of the graph is defined by predefined color models and logarithmic distance transform map. Finally, the object is extracted by minimizing the energy. Experimental results of various test images show that our algorithm works more accurately than other methods.

• The Transactions of the Korea Information Processing Society
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• v.6 no.8
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• pp.2124-2132
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• 1999

Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.2
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• pp.359-370
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• 1997

We consider a facility layout problem with the objective of minimizing total transportation distance, which is the sum of rectilinear distances between facilities weighted by the frequency of trips between the facilities. It is assumed that facilities are required to have rectangular shapes and there is no empty space between the facilities in the layout. In this study, a graph theoretic heuristic is developed for the problem. In the heuristic, planar graphs are constructed to represent adjacencies between the facilities and then the graphs are converted to block layouts on a continual plane using a layout construction module. (Therefore, each graph corresponds to a layout.) An initial layout is obtained by constructing a maximal weighted planar graph and then the layout is improved by changing the planar graph. A simulated annealing algorithm is used to find a planar graph which gives the best layout. To show the performance of the proposed heuristic, computational experiments are done on randomly generated test problems and results are reported.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.418-418
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• 2000

This paper proposes a path planning algorithm for mobile robot. To generate an optimal path and minimum time path for a mobile robot, we use the Genetic Algorithm(GA) and Visibility Graph. After finding a minimum-distance between start and goal point, the path is revised to find the minimum time path by path-smoothing algorithm. Simulation results show that the proposed algorithms are more effective.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.5
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• pp.398-409
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• 2013

This paper provides an overview of distance-based formation control. Firstly, in this paper, we introduce preliminary background materials that are used in defining the distance-based formation control. Then, based on the preliminary background, we briefly review main results developed thus far in this field. Lastly, we provide some issues that need to be studied further in future works.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.666-668
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• 1998

In this paper, we consider a bi-objective vehicle routing problem to minimize total distance traveled and maximize minimum integrated satisfaction level of selecting desirable routes in an fuzzy graph. The fuzzy graph reflects a real delivery situation in which there are a depot, some demand points, paths linking them, and distance and integrated satisfaction level are associated with each route. For solving the vi-objective problem we introduce a concept of routing vector and define non-dominated solution for comparing vectors. An efficient algorithm involving a selection method of non-dominated solutions based on DEA is proposed for the vehicle routing problem with rigid distance and integrated satisfaction level.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2732-2734
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• 2000

This paper proposes a path planning algorithm for mobile robots. To generate a minimum-distance path for mobile robots, we use the Genetic Algorithm(GA) and Visibility Graph. After finding a minimum-distance path between a start and a goal point, the path is revised to find the smooth subminimum-distance path by a path-smoothing algorithm. Simulation results show that the proposed algorithms are effective.

• Journal of the Korea Society of Computer and Information
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• v.19 no.5
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• pp.19-25
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• 2014

In this paper, I seek the chromatic number, the maximum number of colors necessary when adjoining vertices in the plane separated apart at the distance of 1 shall receive distinct colors. The upper limit of the chromatic number has been widely accepted as $4{\leq}{\chi}(G){\leq}7$ to which Hadwiger-Nelson proposed ${\chi}(G){\leq}7$ and Soifer ${\chi}(G){\leq}9$ I firstly propose an algorithm that obtains the minimum necessary chromatic number and show that ${\chi}(G)=3$ is attainable by determining the chromatic number for Hadwiger-Nelson's hexagonal graph. The proposed algorithm obtains a chromatic number of ${\chi}(G)=4$ assuming a Hadwiger-Nelson's hexagonal graph of 12 adjoining vertices, and again ${\chi}(G)=4$ for Soifer's square graph of 8 adjoining vertices. assert. Based on the results as such that this algorithm suggests the maximum chromatic number of a planar graph is ${\chi}(G)=4$ using simple assigned rule of polynomial time complexity to color for a vertex with minimum degree.

• IEMEK Journal of Embedded Systems and Applications
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• v.7 no.2
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• pp.71-78
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• 2012

Based on the Zigbee-based wireless sensor network, I suggest the way to reduce errors between the short distance, improving the accuracy of the presumed distance by revising the deviation of RSSI(Received Signal Strength Indication) values is to estimate the distance using only the RF signal power without the additional hardware. In general, the graph measured by RSSI values shows the proximity values which are ideally reduced in proportion to the distance under the free outdoor space in which LOS(Line-Of-Sight) is guaranteed. However, if the result of the received RSSI values are each substituted to the formula, it can produce a larger margin of error and less accurate measurement since it is based upon the premise that this free space is not affected by reflected waves or obstacles caused by the ground and electronic jamming engendered by the environment. Therefore, the purpose of this study is to reduce the margin of errors between the distances and to measure the proximity values with the ideal type of graph by suggesting the way to revise the received RSSI values in the light of these reflected waves or obstacles and the electronic jamming. In conclusion, this study proves that errors are reduced by comparing the proposed deviation correction method to the revised RSSI value.