• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.379-395
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• 2018

Assume that R is a commutative ring with non-zero identity which is not an integral domain. An ideal I of R is called an annihilating ideal if there exists a non-zero element $a{\in}R$ such that Ia = 0. S. Visweswaran and H. D. Patel associated a graph with the set of all non-zero annihilating ideals of R, denoted by ${\Omega}(R)$, as the graph with the vertex-set $A(R)^*$, the set of all non-zero annihilating ideals of R, and two distinct vertices I and J are adjacent if I + J is an annihilating ideal. In this paper, we study the relations between the diameters of ${\Omega}(R)$ and ${\Omega}(R[x])$. Also, we study the relations between the diameters of ${\Omega}(R)$ and ${\Omega}(R[[x]])$, whenever R is a Noetherian ring. In addition, we investigate the relations between the diameters of this graph and the zero-divisor graph. Moreover, we study some combinatorial properties of ${\Omega}(R)$ such as domination number and independence number. Furthermore, we study the complement of this graph.

• Industrial Engineering and Management Systems
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• v.9 no.3
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• pp.227-241
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• 2010

A memory module industry's supply chain usually consists of multiple manufacturing sites and multiple distribution centers. In order to fulfill the variety of demands from downstream customers, production planners need not only to decide the order allocation among multiple manufacturing sites but also to consider memory module industrial characteristics and supply chain constraints, such as multiple material substitution relationships, capacity, and transportation lead time, fluctuation of component purchasing prices and available supply quantities of critical materials (e.g., DRAM, chip), based on human experience. In this research, a directed graph-based supply network planning (DGSNP) model is developed for memory module industry. In addition to multi-site order allocation, the DGSNP model explicitly considers production planning for each manufacturing site, and purchasing planning from each supplier. First, the research formulates the supply network's structure and constraints in a directed-graph form. Then, a proposed genetic algorithm (GA) solves the matrix form which is transformed from the directed-graph model. Finally, the final matrix, with a calculated maximum profit, can be transformed back to a directed-graph based supply network plan as a reference for planners. The results of the illustrative experiments show that the DGSNP model, compared to current memory module industry practices, determines a convincing supply network planning solution, as measured by total profit.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.679-684
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• 2015

In this paper we discuss bounds for the total curvature of nonparametric minimal surfaces by using the properties of planar harmonic mappings.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.171-186
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• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.12
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• pp.2410-2418
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• 2015

In this paper, we consider the femto users and their mutual interference as graph elements, nodes and weighted edges, respectively. The total bandwidth is divided into a number of resource blocks (RBs) and these are assigned to the femto user equipment (FUEs) using a graph coloring algorithm. In addition, resources blocks are assigned to the femto users to avoid inter-cell interference. The proposed scheme is compared with the traditional scheduling schemes in terms of throughput and fairness and performance improvement is achieved by exploiting the graph coloring scheme.

• 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 Korean Elementary Science Education
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• v.31 no.4
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• pp.490-500
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• 2012

This study was to examine elementary male and female students' spatial abilities, science process skills, and graph construction and interpretation abilities in order to understand the effect that their spatial abilities and science process skills would have on their graph abilities. To conduct this study, total 12 classes of 435 pupils, 6 classes each from grades 5 and 6 in elementary schools were selected for subjects. The number of male student was 207 and that of female one was 228 of them. And previous test papers of spatial abilities, of science process abilities, and of graph abilities were retouched and updated for reuse in new tests. The results of this study are briefed as follows: Firstly, when spatial abilities for male and female group were compared, female group showed a little higher rate of correct answering than male, but not providing statistically significant gap. Secondly, the science process skill tests revealed basic process skills of both groups were more excellent than their integrated process skills, while female group was found to have more correct answers than male, all of which were proving statistical distinction. Thirdly, of graphing skills for two groups, the graph interpretation skills turned out to be better than the graph construction skills, with female group scoring higher than male and with meaningful difference. Fourthly, both between spatial abilities and graph abilities, and between science process skills and graph abilities, static correlations existed with statistical meaning. In other words, those with higher spatial abilities or science process skills were to do better in constructing and interpreting graphs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.4A
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• pp.350-359
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• 2010

In this paper, we provide a subchannel allocation algorithm for a femtocell system with OFDMA. This algorithm aims to maximize the minimum number of allocated subchannels among all femtocells and in addition, to maximize the total usage of subchannels in all femtocells. The subchannel allocation algorithm consists of three steps: constructing an interference graph, coloring algorithm, and mapping subchannels to colors. In the first step, the femtocell system is modelled by an interference graph, in which each femtocell is modeled as a node and two nodes that interfere with each other are connected by an edge. Based on this interference graph, by using a coloring scheme and mapping subchannels to each color, we can allocate subchannels to each femtocell. Finally, the performance of this algorithm is provided by simulation.

• Journal of the Korea Society of Computer and Information
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• v.23 no.3
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• pp.85-92
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• 2018

We consider a project scheduling problem in which the jobs can be compressed by using additional resource to meet the corresponding due dates, referred to as a time-cost tradeoff problem. The project consists of two independent subprojects of which precedence graph is a chain. The due dates of jobs constituting the project can be interpreted as the multiple assessments in the life of project. The penalty cost occurs from the tardiness of the job, while it may be avoided through the compression of some jobs which requires an additional cost. The objective is to find the amount of compression that minimizes the total tardy penalty and compression costs. Firstly, we show that the problem can be decomposed into several subproblems whose number is bounded by the polynomial function in n, where n is the total number of jobs. Then, we prove that the problem can be solved in polynomial time by developing the efficient approach to obtain an optimal schedule for each subproblem.

• Management Science and Financial Engineering
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• v.22 no.1
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.