• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.11
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• pp.634-639
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• 2002

A Shortest Path Algorithm is the method to find the most efficient route among many routes from a start node to an end node. It is based on Labeling methods. In Labeling methods, there are Label-Setting method and Label-Correcting method. Label-Setting method is known as the fastest one among One-to-One shortest path algorithms. But Benjamin[1,2] shows Label-Correcting method is faster than Label-Setting method by the experiments using large road data. Since Graph Growth algorithm which is based on Label-Correcting method is made to find One-to-All shortest path, it is not suitable to find One-to-One shortest path. In this paper, we propose a new One-to-One shortest path algorithm. We show that our algorithm is faster than Graph Growth algorithm by extensive experiments.

• Journal of Digital Convergence
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• v.12 no.11
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• pp.309-316
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• 2014

In this paper, we propose an efficient detph map creation method using Graph Cut and Discrete Wavelet Transform. First, we have segmented the original image by using Graph Cut to process with its each areas. After that, the information which describes segmented areas of original image have been created by proposed labeling method for segmented areas. And then, we have created four subbands which contain the original image's frequency information. Finally, the depth map have been created by frequency map which made with HH, HL subbands and depth information calculation along the each segmented areas. The proposed method can perform efficient depth map creation process because of dynamic allocation using depth information. We also have tested the proposed method using PSNR(Peak Signal to Noise Ratio) method to evaluate ours.

• Korean Journal of Community Nutrition
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• v.8 no.2
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• pp.220-230
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• 2003

The purpose of this study was to investigate consumer preferred formats of nutrition labels: the type of nutritional information provided on the labels. A survey was conducted on 222 housewives between the age of 20 and 65 in Daejeon city in 1998, using an interview questionnaire showing illustrated nutritional label formats. Among twelve nutrients and caloric values listed on the nutrition labels, the housewives ranked their interest in the items in the following order of calorie (58.56%), calcium (56.76%), cholesterol (54.05%), protein (39.19%) and vitamin C (36.04%). The majority of the subjects (69.37%) checked labels when they bought milk or dairy products, whereas only 8.11% looked at labels when they bought Ramyon or noodles. Most of the subjects (90.99%) preferred products with labels with nutritional information as compared with products without labels. this was especially so true of the younger individuals and of pc-ople who checked food labels more frequently. The subjects preferred labeling which described the nutrient content per Package (55.41%), sewing size (32.88%) and food weight of 1009 (11.71%) as a standard nit. Generally, they prefer-red a simplified list to a detailed list of the number of nutrients, a figure graph to bar graph in nutrition claim, vertical bar graph to horizontal bar graph showing the nutritional content of foods and a web-type graphic format to a radiation-format when describing the item's percentage of the Korean RDA's nutrient content. The subjects who checked labels frequently especially preferred detailed list, while housewives with job or with unhealthy family members preferred a simplified list and graphic, rather than a numerical display. From this result, it is suggested that providing consumers with more nutrients information in a more easily understood graphic format would encourage the consumers to check nutritional labels. Therefore this should be considered when developing the regulations far nutrition labeling or when educating the Public about nutrition. (Korean J Community Nutrition 8(2) : 220∼230, 2003)

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.9
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• pp.858-862
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• 2015

This paper presents a new forward-viewing mono-camera based obstacle detection algorithm for mobile robots. The proposed method extracts the coarse location of an obstacle in an image using inverse perspective mapping technique from sequential images. In the next step, graph-cut based image labeling is conducted for estimating the exact obstacle boundary. The graph-cut based labeling algorithm labels the image pixels as either obstacle or floor as the final outcome. Experiments are performed to verify the obstacle detection performance of the developed algorithm in several examples, including a book, box, towel, and flower pot. The low illumination condition, low color contrast between floor and obstacle, and floor pattern cases are also tested.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of the Korea Society of Computer and Information
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• v.20 no.7
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• pp.41-47
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• 2015

The bandwidth minimization problem (BMP) has been classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. This paper suggests polynomial time heuristic algorithm is to find the solution of bandwidth minimization problem. To find the minimum bandwidth ${\phi}^*=_{min}{\phi}(G)$, ${\phi}(G)=_{max}\{{\mid}f(v_i)-f(v_j):v_i,v_j{\in}E\}$ for given graph G=(V,E), m=|V|,n=|E|, the proposed algorithm sets the maximum degree vertex $v_i$ in graph G into global central point (GCP), and labels the median value ${\lceil}m+1/2{\rceil}$ between [1,m] range. The graph G is partitioned into subgroup, the maximum degree vertex in each subgroup is set to local central point (LCP), and we adjust the label of LCP per each subgroup as possible as minimum distance from GCP. The proposed algorithm requires O(mn) time complexity for label to all of vertices. For various twelve graph, the proposed algorithm can be obtains the same result as known optimal solution. For one graph, the proposed algorithm can be improve on known solution.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.565-586
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• 2017

In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

• Journal of KIISE:Databases
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• v.32 no.5
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• pp.526-535
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• 2005

Ontology is a methodology on describing specific concepts and their relationships, and it is being considered important more and more as semantic web and variety of knowledge management systems are being highlighted. Ontology uses the relationships among concerts to represent some concrete semantics of specific concept. When we want to get some useful information from ontology, we severely have to process the transitive relationships because most of relationships among concepts represent transitivity. Technically, it causes recursive calls to process such transitive closure queries with heavy costs. This paper describes the efficient technique for processing transitive closure queries in ontology. To the purpose of it, we examine some approaches of current systems for transitive closure queries, and propose a technique by graph labeling scheme. Basically, we assume large size of ontology, and then we show that our approach gives relative efficiency in processing of transitive closure, queries.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.11-21
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• 2008

A graph G = (V, E) is called super edge-magic if there exists a one-to-one map $\lambda$ from V $\cup$ E onto {1,2,3,...,|V|+|E|} such that $\lambda$(V)={1,2,...,|V|} and $\lambda(x)+\lambda(xy)+\lambda(y)$ is constant for every edge xy. In this paper, we investigate whether some families of graphs are super edge-magic or not.