• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.5
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• pp.993-1001
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• 2003

A RDB Storage Model based on the Edge-Labeled Graph is suggested for store the XML instance in Relational Databases(RDB). The XML instance being stored is represented by Data Graph based on the Edge-Labeled Graph. Data Path Table, Element, Attribute, and Table Index Table values are extracted. Then Database Schema is defined, and the extracted values are stored using the Mapper. In order to support querry, Repository Model offers the translator translating XQL which is used as query language under XPATH, into SQL. In addition, it creates DBtoXML generator restoring the stored XML instance. As a result, storage relationship between the XML instance and proposed model structure can be expressed in terms of Graph-based Path, and it shows the possibility of easy search of random Element and Attribute information.

• Journal of Internet Computing and Services
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• v.4 no.6
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• pp.33-42
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• 2003

A XML Instance repository model based on the Edge-Labeled Graph is suggested for storing the XML instance in Relational Databases, This repository model represents the XML instance as a data graph based on the Edge-Labeled Graph, extracts the defined value based on the structure of data path, element, attribute, and table index table presented as database schema, and stores these values using the Mapper module, In order to support querry, XML repository model offers the module translating XQL which is a query language under XPATH to SQL, and has DBtoXML generator module restoring the stored XML instance. As a result, it is possible to represent the storage relationship between the XML instances and the proposed repository model in terms of Graph-based Path, and it shows the possibility of easy search of specific element and attribute information.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.545-547
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• 2003

본 논문에서는 Edge-Labeled Graph에 기반하여 XML 인스턴스들을 관계형 데이터베이스(RDB)로 저장하는 모델을 제안하고 구현한다. 저장되는 XML 인스턴스들은 Edge-Libeled Graph에 기반 한 Data Graph로 표현되고 이를 이용하여 데이터 경로(Data Path), 요소(Element), 속성(Attribute), 테이블 인덱스(Table Index) 테이블에 정의된 값들이 추출된 후 Napper를 이용하여 데이터베이스 스키마를 정의하고 추출된 값들을 저장한다. 그리고, RDB 저장 모델은 질의를 지원하기 위해, XPATH를 따르는 질의 언어로 사용되는 XQL을 SQL로 변환하는 변환기를 제공하며, 또한 저장된 XML 인스턴스를 복원하는 DBtoXML 처리기를 갖도록 하였다. 구현 결과, XML 인스턴스들과 RDB 구조로의 저장 관계가 그래프(Graph) 기반의 경로(Path)를 이용한 표현으로 가능했으며, 동시에, 특정 요소 (Element) 또는 속성(Attribute)들의 정보들을 쉽게 검색할 수 있는 가능성을 보였다.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.223-237
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• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.615-631
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• 2023

A power cordial labeling of a graph G = (V (G), E(G)) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge e = uv is assigned the label 1 if f(u) = (f(v))ⁿ or f(v) = (f(u))ⁿ, For some n ∈ ℕ ∪ {0} and the label 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we investigate power cordial labeling for helm graph, flower graph, gear graph, fan graph and jewel graph as well as larger graphs obtained from star and bistar using graph operations.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.40 no.5
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• pp.429-437
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• 2022

Recently, the demand for a QA (Question Answering) system for human-machine communication has increased. Among the QA systems, a closed domain QA system that can handle spatial-related questions is called GeoQA. In this study, a new type of graph database, LPG (Labeled Property Graph) was used to overcome the limitations of the RDF (Resource Description Framework) based database, which was mainly used in the GeoQA field. In addition, GraphQL (Graph Query Language), an API-type query language, is introduced to address the fact that the LPG query language is not standardized and the GeoQA system may depend on specific products. In this study, database was built so that answers could be retrieved when spatial-related questions were entered. Each data was obtained from the national spatial information portal and local data open service. The spatial relationships between each spatial objects were calculated in advance and stored in edge form. The user's questions were first converted to GraphQL through FOL (First Order Logic) format and delivered to the database through the GraphQL server. The LPG used in the experiment is Neo4j, the graph database that currently has the highest market share, and some of the built-in functions and QGIS were used for spatial calculations. As a result of building the system, it was confirmed that the user's question could be transformed, processed through the Apollo GraphQL server, and an appropriate answer could be obtained from the database.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.237-253
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• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.731-734
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• 2000

We present a novel graph labeling problem called Fibonacci edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be (3m+2)-th Fibonacci numbers. We show that every Fibonacci tree can be labeled Fibonacci edge labeling. The labelings on the Fibonacci trees are applied to their embeddings into Fibonacci Circulants.