• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.85-98
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• 2012

Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.149-154
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• 2024

This paper proposes an algorithm that remedy Floyd's the tortoise and the hare algorithm (THA) shortcomings which is specialized in singly linked list (SLL), so this algorithm fails to detect the cycle in undirected graph, digraph, and tree with multiple inputs or outputs. The proposed algorithm simply pruning the source and sink with only one edge using cycle detection of single edge node pruning. As a result of the experimental of various list, undirected graph, digraph, and tree, the proposed algorithm can be successively detect the cycle all of them. Thus, the proposed algorithm has the simplest and fastest advantage in the field of cycle detection.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.1
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• pp.143-152
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• 2013

Given weighted graph G=(V,E), n=|V|, m=|E|, the minimum cut problem is classified with source s and sink t or without s and t. Given undirected weighted graph without s and t, Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs $\frac{n(n-1)}{2}$ times. Given graph with s and t, Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from s to t. If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with s and t. This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs n-1 times and successfully divides V into disjoint S and V sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within n-1 processing times.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.119-124
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• 2002

We consider a multi-state flow network consisted of undirected links and focus on how to find efficiently the union of minimal paths transmitting a required flow when minimal paths are known.

• Proceedings of the Korean Society of Computer Information Conference
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• 2015.01a
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• pp.167-168
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• 2015

유전자 알고리즘은 문제 크기가 커짐에 따라 해집합이 폭발적으로 늘어나 최적해를 찾기 힘든 최적화 문제에 주로 적용되는 알고리즘으로, 최근에는 지리정보시스템(GIS)의 경로 최적화 문제, 게임에서의 길찾기, 인공지능에 많이 적용되고 있다. 마이크로 유전자 알고리즘은 일반 유전자 알고리즘에 비해 작은 크기의 모집단을 사용함으로써 알고리즘의 효율을 높일 수 있는 장점이 있다. 따라서, 본 논문에서는 무향 Rural Postman Problem 해법으로 마이크로 유전자 알고리즘의 적용 방법을 제안한다.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.75-82
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• 2018

Let P be a commutator poset with Z(P) its set of zero-divisors. The annihilator graph of P, denoted by AG(P), is the (undirected) graph with all elements of $Z(P){\setminus}\{0\}$ as vertices, and distinct vertices x, y are adjacent if and only if $ann(xy)\;{\neq}\;(x)\;{\cup}\;ann(y)$. In this paper, we study basic properties of AG(P).

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.119-123
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• 2009

The minimum multicut problem on a cycle is to find a multicut on an undirected cycle such that the sum of weights is minimized, which is known to be polynomially solvable. This paper shows that there exists a compact polyhedral description of the set of feasible solutions to the problem whose number of variables and constraints is O($\upsilon\kappa$).

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.189-199
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• 1994

This paper considers the covering network design problem (CNDP). In the CNDP, an undirected graph is given where nodes correspond to potential facility sites and arcs to potential links connecting facilities. The objective of the CNDP is to identify the least cost connected subgraph whose nodes cover the given demand points. The problem difines a demand point to be covered if some node in the selected graph is present within an appropriate distance from the demand point. We present an integer programming formulation for the problem and develop a dual-based solution procedure. The computational results for randomly generated test problems are also shown.

• Management Science and Financial Engineering
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• v.15 no.1
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• pp.71-79
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• 2009

This paper considers the two kinds of integer multicommodity flow problems, a feasibility problem and a maximization problem, on two types of directed cycles, a unidirectional and a bidirectional cycle. Both multicommodity flow problems on an undirected cycle have been dealt with by many researchers and it is known that each problems can be solved by a polynomial time algorithm. However, we don't find any result on the directed cycles. Here we show that we can also solve both problems for a unidirectional and a bidirectional cycle in polynomial time.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.213-217
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• 2012

Fuzzy k-means clustering is an attractive alternative to the ordinary k-means clustering in analyzing multivariate data. Fuzzy versions yield more natural output by allowing overlapped k groups. In this study, we modify a fuzzy k-means clustering algorithm to be used for undirected social networks, apply the algorithm to both real and simulated cases, and report the results.