• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.683-714
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• 2016

In this paper we investigate the toroidality of the comaximal graph of a finite lattice.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.81-105
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• 2018

In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: we find a polynomial time algorithm to decide if a given reflexive graph G, in which no two vertices have the same neighbourhood, admits a distributive lattice polymorphism.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.433-451
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• 2018

In this paper, we study the toroidality of the comaximal graphs of a finite lattice.

• Journal of Internet Computing and Services
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• v.7 no.5
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• pp.109-121
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• 2006

In this paper, we suggest lattice based role graph security management model which changes security level in mandatory access control model as well as constraint and role hierarchy systematically in role base access control model. In this model, we solved privilege abuse of senior role that is role graph model's problem, and when produce conflict between privileges, we can keep integrity of information by reseting grade of subject through constraint. Also, we offer strong security function by doing to be controlled by subject's security level as well as privilege inheritance by role hierarchy, Finally, we present the role graph algorithms with logic to disallow roles that contain conflicting privileges.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.2
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• pp.9-16
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• 2004

Recently, lattice conditional independence models(LCIMs) have been introduced for the analysis of non-monotone missing data patterns and of non-nested dependent regression models. This approach has been successfully applied to solve various problems in data pattern analysis, however, it suffers from computational burden to search LCIMs. In order to cope with this drawback, we propose a new scheme for finding LCIMs based on the essential graph. Also, we show that the class of LCIMs coincides with the class of all transitive acyclic directed graph(TADG) models which are Markov equivalent to a specific acyclic directed graph(ADG) models.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• Journal of the Korea Society of Computer and Information
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• v.14 no.6
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• pp.91-98
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• 2009

In this paper, this model ensures confidentiality and integrity of mandatory access cotrol policy which based on fuzzy function with importance of information. And it solves authorization abuse problem through role graph creation algorithm and flowing policy that security grade is applied. Because this model composes role hierarchy which bind similar role concept to apply to commercial environment, it has expansile advantage by large scale security system as well as is easy that add new role.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.2
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• pp.228-234
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• 2006

This paper describes a systematic process which can generate a complete circuit specification efficiently for a given recursive DSP algorithm based on an optimal multiprocessor scheduler. The process is composed of two states: scheduling and circuit synthesis. The scheduling part accepts a fully specified flow graph(FSFG) as an input, and generates an optimal synchronous multiprocessor schedule. Then the circuit synthesis part translates the modified schedule into a complete circuit diagram including a control specification. The circuit diagram can be applied to a silicon compiler for VLSI layout generation. This paper illustrates the whole process with an example of a second order Gray-Market lattice filter.

• 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.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.81-96
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• 2015

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if $H{\cap}K{\neq}1$ where 1 denotes the trivial subgroup of G. In this paper we characterize all finite groups whose intersection graphs are planar. Our methods are elementary. Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroup graph of a group, each of whose planarity was already considered before in [2, 10, 11, 12].