• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.977-986
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• 2015

Let G be a graph on the vertex set $V(G)=\{x_1,{\cdots},x_n\}$ with the edge set E(G), and let $R=K[x_1,{\cdots},x_n]$ be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials $x_i,x_j$ with $\{x_i,x_j\}{\in}E(G)$, and the vertex cover ideal $I_G$ generated by monomials ${\prod}_{x_i{\in}C}{^{x_i}}$ for all minimal vertex covers C of G. A minimal vertex cover of G is a subset $C{\subset}V(G)$ such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers $L_G$ and we explicitly describe the minimal free resolution of the ideal associated to $L_G$ which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.649-657
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• 2000

The 2-step competition graph of D has the same vertex set as D and an edge between vertices x and y if and only if there exist (x, z)-walk of length 2 and (y, z)-walk of length 2 for some vertex z in D. The 2-step competition number of a graph G is the smallest number k such that G together with k isolated vertices is the 2-step competition graph of an acyclic digraph. Cho, et al. showed that the 2-step competition number of a path of length at least two is two. In this paper, we characterize all the minimal acyclic digraphs whose 2-step competition graphs are paths of length n with two isolated vertices and construct all such digraphs.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.409-439
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• 2021

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a partial matching, and the lattice polytope associated with a pair of lattice presentations, and we investigate transformations with minimal area.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.594-617
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• 2022

In this study, firstly Smarandache ruled surfaces whose base curves are Smarandache curves derived from Frenet vectors of the curve, and whose direction vectors are unit vectors plotting Smarandache curves, are created. Then, the Gaussian and mean curvatures of the obtained ruled surfaces are calculated separately, and the conditions to be developable or minimal for the surfaces are given. Finally, the examples are given for each surface and the graphs of these surfaces are drawn.

• Journal of Information Technology Applications and Management
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• v.17 no.1
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• pp.11-33
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• 2010

The majority of graphs and visuals made publicly available by Thai listed companies tend to be disjointed and minimal. Only a little over fifty percent of the total 478 companies included graphic representations of their business operations and performance in the form of two or three dimensional spreadsheet based graphs in their annual reports, investor relations documents, websites and so on. For novice users, these visual representations are unlikely to give the big picture of what is the company's financial position and performance. Neither will they tell where the company stands in its own operating environment. The existing graphics and visuals, in very rare cases, can provide a sense of the company's future outlook. For boundary users such as audit committees whose duty is to promote good governance through transparency and disclosure, preliminary interview results show that there is some doubt as to whether the inclusion of big-picture visuals can really be of use to minority shareholders. These boundary users expect to see more insightful visuals beyond those produced by traditional spreadsheets which will enable them to learn to cope with the on-going turbulence in today's business environment more quickly. However, the debate is still going on as to where to draw the line between internal or external reporting visuals.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.1
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• pp.42-49
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• 1987

This paper describes test-pattern generation and it;s sequence for fan out-free Combinational logic network with multiple faults. The method for detecting multiple faults, in systematic way, is established by using characteristic graphs. This method is applied even in the case of fan out-reconvergent combinational logic networks. In this case, the network is decomposed into a set of fan out-free sybnetworks so as to use the characteristic graphs, and minimal test patterns are generated seperately. The each test set is combined and the test pattern for fan out-reconvergent networks are derived. According to corresponding characteristic graph, additional test patterns to detect multiple faults are simply derived.

• The Transactions of the Korea Information Processing Society
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• v.7 no.5
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• pp.1464-1473
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• 2000

In this paper, we analyze the cycle property of the (n,k)-star graph that has an attention as an alternative interconnection network topology in recent years. Based on the graph-theoretic properties in (n,k)-star graphs, we show the pancyclic property of the graph and also present the corresponding algorithm. Based on the recursive structure of the graph, we present such top-down approach that the resulting cycle can be constructed by applying series of "dimension expansion" operations to a kind of cycles consisting of sub-graphs. This processing naturally leads to such property that the resulting cycles tend to be integrated compactly within some minimal subset of sub-graphs, and also means its applicability of another classes of the disjoint-style cycle problems. This result means not only the graph-theoretic contribution of analyzing the pancyclic property in the underlying graph model but also the parallel processing applications such a as message routing or resource allocation and scheduling in the multi-computer system with the corresponding interconnection network.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.415-430
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• 2018

A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycle. A graph G is acyclically L-list colorable if for a given list assignment $L=\{L(v):v{\in}V(G)\}$, there exists an acyclic coloring ${\phi}$ of G such that ${\phi}(v){\in}L(v)$ for all $v{\in}V(G)$ A graph G is acyclically k-choosable if G is acyclically L-list colorable for any list assignment with $L(v){\geq}k$ for all $v{\in}V(G)$. Let G be a planar graph without 5-cycles and adjacent 4-cycles. In this article, we prove that G is acyclically 5-choosable if every vertex v in G is incident with at most one i-cycle, $i {\in}\{6,7\}$.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.529-532
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• 1988

This paper proposes a graph matching algorithm based on simulated annealing, which assures the globally optimal solution for circuit partitioning for the placement in the rectilinear region occurring as a result of the pre-placement of some macro cells, or onto the nonplanar surface in some military or space applications. The circuit graph ($G_{C}$) denoting the circuit topology is formed by a hierarchical bottom-up clustering of cells, while another graph called region graph ($G_{R}$) represents the geometry of a planar rectilinear region or a nonplanar surface for circuit placement. Finding the optimal many-to-one vertex mapping function from $G_{C}$ to $G_{R}$, such that the total mismatch cost between two graphs is minimal, is a combinatorial optimization problem which was solved in this work for various examples using simulated annealing.

• Korean Journal of Clinical Pharmacy
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• v.10 no.1
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• pp.38-41
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• 2000

A high-performance liquid chromatographic method with fluorometric detection was evaluated for analysis of ofloxacin in plasma. Biological fluids (plasma, $200\;{\mu}L$) were prepared for assay by protein precipitation with chlorofurm. The detection of ofloxacin and triamterene as an internal standard were performed at 358 nm for excitation and 495 nm for emission. The HPLC separation was carried out on Ultrasphere ODS column (4.6 mm${\times}25\;cm,\;5\;{\mu} m$) with acetonitrile $(45\%)$-phosphoric acid $(1.5\%)\;containing\;0.3\%$ sodium laurylsulfate as the mobile phase. The flow-rate was 1.0 mL/min. The calibration graphs were linear from 3.0 to 80 ng/mL with r=0.998. The minimal detectable concentration in plasma was 1.5 ng/mL. The proposed technique is reproducible, selective, reliable and sensitive.