• East Asian mathematical journal
• /
• 제35권1호
• /
• pp.17-22
• /
• 2019

A travel groupoid is a pair (V, ${\ast}$) of a set V and a binary operation ${\ast}$ on V satisfying two axioms. For a travel groupoid, we can associate a graph in a certain manner. For a given graph G, we say that a travel groupoid (V, ${\ast}$) is on G if the graph associated with (V, ${\ast}$) is equal to G. There are some results on the classification of travel groupoids which are on a given graph [1, 2, 3, 9]. In this article, we introduce the notion of vertex-indexed partition systems on a graph, and classify the travel groupoids on the graph by the those vertex-indexed partition systems.

• 대한산업공학회지
• /
• 제28권3호
• /
• pp.264-273
• /
• 2002

This paper focuses on disassembly sequencing, which is the problem of determining the optimum disassembly level and the corresponding disassembly sequence for a product at its end-of-life with the objective of maximizing the overall profit. In particular, sequence-dependent operation times, which frequently occur in practice due to tool-changeover, part reorientation, etc, are considered in the parallel disassembly environment. To represent the problem, a modified directed graph of assembly states is suggested as an extension of the existing extended process graph. Based on the directed graph, the problem is transformed into the shortest path problem and formulated as a linear programming model that can be solved straightforwardly with standard techniques. A case study on a photocopier was done and the results are reported.

• 대한수학회보
• /
• 제44권4호
• /
• pp.651-661
• /
• 2007

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s{\approx}t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s{\approx}t$. A graph G=(V,E) is called an $(xy)x{\approx}x(yy)$ graph if the graph algebra $\underline{A(G)}$ satisfies the equation $(xy)x{\approx}x(yy)$. An identity $s{\approx}t$ of terms s and t of any type ${\tau}$ is called a hyperidentity of an algebra $\underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $\underline{A}$ of the appropriate arity, the resulting identities hold in $\underline{A}$. In this paper we characterize $(xy)x{\approx}x(yy)$ graph algebras, identities and hyperidentities in $(xy)x{\approx}x(yy)$ graph algebras.

• Nuclear Engineering and Technology
• /
• 제48권2호
• /
• pp.386-403
• /
• 2016

The safety of nuclear power plants is analyzed by a probabilistic risk assessment, and the fault tree analysis is the most widely used method for a risk assessment with the event tree analysis. One of the well-known disadvantages of the fault tree is that drawing a fault tree for a complex system is a very cumbersome task. Thus, several graphical modeling methods have been proposed for the convenient and intuitive modeling of complex systems. In this paper, the reliability graph with general gates (RGGG) method, one of the intuitive graphical modeling methods based on Bayesian networks, is improved for the reliability analyses of dynamic systems that have various operation modes with time. A reliability matrix is proposed and it is explained how to utilize the reliability matrix in the RGGG for various cases of operation mode changes. The proposed RGGG with a reliability matrix provides a convenient and intuitive modeling of various operation modes of complex systems, and can also be utilized with dynamic nodes that analyze the failure sequences of subcomponents. The combinatorial use of a reliability matrix with dynamic nodes is illustrated through an application to a shutdown cooling system in a nuclear power plant.

• 대한수학회논문집
• /
• 제26권2호
• /
• pp.291-296
• /
• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Journal of applied mathematics & informatics
• /
• 제33권5_6호
• /
• pp.545-557
• /
• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• 전자공학회논문지A
• /
• 제33A권2호
• /
• pp.196-204
• /
• 1996

This paper presents a new scheduling algorithm, which is the most improtant subtask in the high level synthesis. The proposed algorithm performs scheduling in consideration of resource sharing concept based on characteristics of conditionsla bransches in the intermediate data structure. CDFG (control data flow graph) generated by a VHDL analyzer. This algorithm constructs a conditon graph based on time frame of each operation using both the ASAP and the ALAP scheduling algorithm. The conditon priority is obtained from the condition graph constructed from each conditional brance. The determined condition priority implies the sequential order of transforming the CDFG with conditonal branches into the CDFG without conditional branches. To minimize resource cost, the CDFG with conditional branches are transformed into the CDFG without conditonal brancehs according to the condition priority. Considering the data dependency, the hardware constraints, and the data execution time constraints, each operation in the transformed CDFG is assigned ot control steps. Such assigning of unscheduled operations into contorl steps implies the performance of the scheduling in the consecutive movement of operations. The effectiveness of this algorithm is hsown by the experiment for the benchmark circuits.

• Kyungpook Mathematical Journal
• /
• 제61권1호
• /
• pp.61-74
• /
• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• 대한의용생체공학회:의공학회지
• /
• 제38권2호
• /
• pp.82-88
• /
• 2017

Enlargement of the lateral ventricles have been identified as a surrogate marker of neurological disorders. Quantitative measure of the lateral ventricle from MRI would enable earlier and more accurate clinical diagnosis in monitoring disease progression. Even though it requires an automated or semi-automated segmentation method for objective quantification, it is difficult to define lateral ventricles due to insufficient contrast and brightness of structural imaging. In this study, we proposed a fully automated lateral ventricle segmentation method based on a graph cuts algorithm combined with atlas-based segmentation and connected component labeling. Initially, initial seeds for graph cuts were defined by atlas-based segmentation (ATS). They were adjusted by partial volume images in order to provide accurate a priori information on graph cuts. A graph cuts algorithm is to finds a global minimum of energy with minimum cut/maximum flow algorithm function on graph. In addition, connected component labeling used to remove false ventricle regions. The proposed method was validated with the well-known tools using the dice similarity index, recall and precision values. The proposed method was significantly higher dice similarity index ($0.860{\pm}0.036$, p < 0.001) and recall ($0.833{\pm}0.037$, p < 0.001) compared with other tools. Therefore, the proposed method yielded a robust and reliable segmentation result.

• 한국정보과학회논문지:데이타베이스
• /
• 제41권4호
• /
• pp.242-248
• /
• 2014

RDF 데이터가 급속히 증가함에 따라 RDF데이터로부터 정보를 효율적으로 추출하는 기술의 중요성도 점차 커지고 있다. RDF데이터 질의를 위해 가장 많이 사용하는 질의언어인 SPARQL은 문법이 간단하고 그래프 패턴을 손쉽게 질의로 표현할 수 있는 장점이 있다. 그러나 사용자가 적절한 SPARQL을 작성하려면 데이터 셋에 대한 온톨로지 구조와 용어를 사전에 파악해야 한다. 이 연구에서는 데이터 셋으로부터 사전에 추출된 스키마정보를 이용한 그래프 질의 생성 및 처리방법을 제안한다. 제안된 방법에서 사용자는 RDF 데이터 셋에 대한 온톨로지 구조 사전파악 없이 화면상에서 동적으로 질의를 작성하여 정보를 조회할 수 있다. 사용자가 생성한 질의는 관계형데이터베이스에 저장된 트리플 데이터에 대해 그래프 탐색을 수행할 때 탐색공간 제약조건으로 활용된다. LUBM(10,0) 데이터 셋에 대하여 LUBM 질의 2, 8, 9번을 이용하여 질의 처리 성능과 완전성을 확인하였다.