• Title, Summary, Keyword: Graph theory

### Fuzzy ideal graphs of a semigroup

• Rao, Marapureddy Murali Krishna
• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.363-371
• /
• 2018
• The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

### CAS IMPLEMENTATION OF RECURSIVE STRUCTURE IN A SPANNING TREE

• Song, Kee-Hong
• East Asian mathematical journal
• /
• v.21 no.2
• /
• pp.249-260
• /
• 2005
• Experimentation using computer plays an important part in education and research in graph theory. The purpose of this paper is to develop the CAS techniques for the hands-on approach in graph theory specifically on the topic of constructing the spanning tree. This paper discusses the advantages of CAS as the software system for doing graph theory and introduces the software solutions integrating multimedia user interface developed by the author, which extend the functionality of the existing CAS-based graph theory software package.

### A Study on the Constructing the Function using Extension Edge Valued Graph (모서리값 확장 그래프를 사용한 함수구성에 관한연구)

• Park, Chun-Myoung
• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.17 no.4
• /
• pp.863-868
• /
• 2013
• In recently years, many digital logic systems based on graph theory are analyzed and synthesized. This paper presented a method of constructing the function using edge valued extension graph which is based on graph theory. The graph is applied to a new data structure. from binary graph which is recently used in constructing the digital logic systems based on the graph theory. We discuss the mathematical background of literal and reed-muller expansion, and we discuss the edge valued extension graph which is the key of this paper. Also, we propose the algorithms which is the function derivation based on the proposed edge valued extension graph. That is the function minimization method of the n-variables m-valued functions and showed that the algorithm had the regularity with module by which the same blocks were made concerning about the schematic property of the proposed algorithm.

### Time-Series Causality Analysis using VAR and Graph Theory: The Case of U.S. Soybean Markets (VAR와 그래프이론을 이용한 시계열의 인과성 분석 -미국 대두 가격 사례분석-)

• Park, Hojeong;Yun, Won-Cheol
• Environmental and Resource Economics Review
• /
• v.12 no.4
• /
• pp.687-708
• /
• 2003
• The purpose of this paper is to introduce time-series causality analysis by combining time-series technique with graph theory. Vector autoregressive (VAR) models can provide reasonable interpretation only when the contemporaneous variables stand in a well-defined causal order. We show that how graph theory can be applied to search for the causal structure In VAR analysis. Using Maryland crop cash prices and CBOT futures price data, we estimate a VAR model with directed acyclic graph analysis. This expands our understanding the degree of interconnectivity between the employed time-series variables.

### ALGEBRAIC RANKS OF THE FUNDAMENTAL GROUPS OF HIGH DIMENSIONAL GRAPH MANIFOLDS

• Kim, Raeyong
• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.527-535
• /
• 2021
• The fundamental group of a high dimensional graph manifold canonically has a graph of groups structure. We analyze the group action on the associated Bass-Serre tree and study the algebraic ranks of the fundamental groups of high dimensional graph manifolds.

### A Historical Background of Graph Theory and the Computer Representation (그래프 이론의 역사적 배경과 그 컴퓨터 표현)

• Kim Hwa-jun;Han Su-young
• Journal for History of Mathematics
• /
• v.18 no.1
• /
• pp.103-110
• /
• 2005
• This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

### Database Segment Distributing Algorithm using Graph Theory (그래프이론에 의한 데이터베이스 세그먼트 분산 알고리즘)

• Kim, Joong Soo
• Journal of Korea Multimedia Society
• /
• v.22 no.2
• /
• pp.225-230
• /
• 2019
• There are several methods which efficiencies of database are uprise. One of the well-known methods is that segments of database satisfying a query was rapidly accessed and processed. So if it is possible to search completely parallel multiple database segment types which satisfy a query, the response time of the query will be reduced. The matter of obtaining CPS(Completely Parallel Searchable) distribution without redundancy can be viewed as graph theoretic problem, and the operation of ring sum on the graph is used for CPS. In this paper, the parallel algorithm is proposed.

### Development of Array Type Inkjet Printer Maintenance System Using Graph Theory (그래프 이론을 이용한 어레이 타입 잉크젯프린터의 메인터넌스 시스템 개발)

• Jung, Y.G.;Shim, J.K.
• Proceedings of the Korean Society of Precision Engineering Conference
• /
• /
• pp.551-552
• /
• 2008

### An Analysis System for Protein-Protein Interaction Data Based on Graph Theory (그래프 이론 기반의 단백질-단백질 상호작용 데이타 분석을 위한 시스템)

• Jin Hee-Jeong;Yoon Ji-Hyun;Cho Hwan-Gue
• Journal of KIISE:Computer Systems and Theory
• /
• v.33 no.5
• /
• pp.267-281
• /
• 2006
• PPI(Protein-Protein Interaction) data has information about the organism has maintained a life with some kind of mechanism. So, it is used in study about cure research back, cause of disease, and new medicine development. This PPI data has been increased by geometric progression because high throughput methods are developed such as Yeast-two-hybrid, Mass spectrometry, and Correlated mRNA expression. So, it is impossible that a person directly manage and analyze PPI data. Fortunately, PPI data is able to abstract the graph which has proteins as nodes, interactions as edges. Consequently, Graph theory plentifully researched from the computer science until now is able to be applied to PPI data successfully. In this paper, we introduce Proteinca(PROTEin INteraction CAbaret) workbench system for easily managing, analyzing and visualizing PPI data. Proteinca assists the user understand PPI data intuitively as visualizing a PPI data in graph and provide various analytical function on graph theory. And Protenica provides a simplified visualization with gravity-rule.

### An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph (행렬-스타 그래프를 전위 그래프에 일-대-일 사상하는 알고리즘)

• Kim, Jong-Seok;Lee, Hyeong-Ok
• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.18 no.5
• /
• pp.1110-1115
• /
• 2014
• The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph $MS_{2,n}$ can be embedded in a transposition graph $T_{2n}$ with dilation n or less and average dilation 2 or less.