• 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.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.255-266
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• 2014

For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.25-37
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• 2019

Let G be a bipartite graph with (X, Y ) as its bipartition. Let B be a complete bipartite graph with a bipartition ($V_1$, $V_2$) such that $X{\subseteq}V_1$ and $Y{\subseteq}V_2$. A bi-packing of G in B is an injection ${\sigma}:V(G){\rightarrow}V(B)$ such that ${\sigma}(X){\subseteq}V_1$, ${\sigma}(Y){\subseteq}V_2$ and $E(G){\cap}E({\sigma}(G))={\emptyset}$. In this paper, we show that if G is a bipartite graph of order n with girth at least 12, then there is a complete bipartite graph B of order n + 1 such that there is a bi-packing of G in B. We conjecture that the same conclusion holds if the girth of G is at least 8.

• Journal of KIISE:Databases
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• v.27 no.2
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• pp.185-198
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• 2000

Recently the technological advance in the hardware dealing with multimedia data as well as the explosive increase of the volume of multimedia data bring about new interest in the use of multimedia presentations in many application domains. To use multimedia presentations efficiently, the integration of multimedia presentations into DBMS is necessary. This paper presents a multimedia presentatation query language based on contents and query processing techniques. Presently, multimedia presentation authoring tools denote a multimedia presentation using a presentation graph which is a DAG. A Node in the graph is a same type of media stream and edges denote a play-out order and a synchronization way among nodes. The contents of presentations graphs are the information of each stream, the sequential order of the information inside each stream and the play-out order among the streams. GCalculus/S is a calculus-based query language and can deal with the contents of a presentation graph and physical characteristics of multimedia data. It expresses the sequential order of information inside each stream and the play-out order of streams of a presentation graph using temporal operators Next, Connected and Until. O-Algebra, which is object algebra, is extended to process GCalculus/S queries.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.491-500
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• 2014

The base of a signed digraph S is the minimum number k such that for any vertices u, v of S, there is a pair of walks of length k from u to v with different signs. Let K be a signed complete graph of order n, which is a signed digraph obtained by assigning +1 or -1 to each arc of the n-th order complete graph $K_n$ considered as a digraph. In this paper we show that for $n{\geq}3$ the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.287-299
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• 2015

A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order $n{\geq}12$ and size at least ${\lfloor}\frac{11n-18}{2}{\rfloor}$ contains three disjoint theta graphs. As a corollary, every graph of order $n{\geq}12$ and size at least ${\lfloor}\frac{11n-18}{2}{\rfloor}$ contains three disjoint cycles of even length.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.241-257
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• 2013

An automorphism group of a graph is said to be $s$-regular if it acts regularly on the set of $s$-arcs in the graph. A graph is $s$-regular if its full automorphism group is $s$-regular. In the present paper, all $s$-regular cubic graphs of order $10p^3$ are classified for each $s{\geq}1$ and each prime $p$.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1939-1944
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• 2003

This paper presents a global path planning algorithm based on a visibility graph method, and applies additionally various constraints for constructing the reduced visibility graph. The modification algorithm for generating the rounded path is applied to the globally shortest path of the visibility graph using the robot size constraint in order to avoid the obstacle. In order to check the visibility in given 3D map data, 3D CAD data with VRML format is projected to the 2D plane of the mobile robot, and the projected map is converted into an image for easy map analysis. The image processing are applied to this grid map for extracting the obstacles and the free space. Generally, the tree size of visibility graph is proportional to the factorial of the number of the corner points. In order to reduce the tree size and search the shortest path efficiently, the various constraints are proposed. After short paths that crosses the corner points of obstacles lists up, the shortest path among these paths is selected and it is modified to the combination of the line path and the arc path for the mobile robot to avoid the obstacles and follow the rounded path in the environment. The proposed path planning algorithm is applied to the mobile robot LCAR-III.