• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.531-540
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• 2008

We discuss the decomposition problems on circuit graphs and triangular graphs, and show how they can be applied to obtain results on spanning trees or hamiltonian cycles. We also prove that every circuit graph containing no separating 3-cycles can be extended by adding new edges to a triangular graph containing no separating 3-cycles.

• East Asian mathematical journal
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• v.30 no.3
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• pp.311-319
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• 2014

It is shown that, for an even positive integer m with $m{\geq}4$ and arbitrary positive integer k and t, the complete multipartite graph $K_{km+1(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles in such a way that the decomposition is circulant.

• Korean Journal of Microbiology
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• v.39 no.2
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• pp.67-75
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• 2003

One large topic in comparative genomics is to predict functional annotation by classifying protein sequences. Computational approaches for function prediction include protein structure prediction, sequence alignment and domain prediction or binding site prediction. This paper is on another computational approach searching for sets of homologous sequences from sequence similarity graph. Methods based on similarity graph do not need previous knowledges about sequences, but largely depend on the researcher's subjective threshold settings. In this paper, we propose a genome sequence clustering method of iterative testing and graph decomposition, and a simple method to calculate a strict threshold having biochemical meaning. Proposed method was applied to known bacterial genome sequences and the result was shown with the BAG algorithm's. Result clusters are lacking some completeness, but the confidence level is very high and the method does not need user-defined thresholds.

• East Asian mathematical journal
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• v.29 no.3
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• pp.337-347
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• 2013

For an even integer m at least 4 and any positive integer $t$, it is shown that the complete equipartite graph $K_{km(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles for any positive integer ${\kappa}$ under the condition satisfying ${\frac{{(m-1)}^2+3}{4m}}$ < ${\kappa}$. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2010.04a
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• pp.11-13
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• 2010

Combined with the indeterminate boundaries of spatial objects, n:m correspondences makes an object-based matching be a complex problem. In this study, we model the boundary of a polygon object with fuzzy model and describe their overlapping relations as a weighted bipartite graph. Then corresponding pairs including 1:0, 1:1, 1:n and n:m relations are identified using a spectral singular value decomposition.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.625-647
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• 2002

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.2
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• pp.375-382
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• 1996

In this paper, aneffective method for computing source to terminal reliability of network by decomposition is described. A graph is modeled after a network, and decomposed into two subgraphs. A logic product term of one subgraph is computed, and a graph of the other subgraphs is made according to the event representing the logic product term, and it's logic product term is compted. By multiplying the logic product term of one subgraph by that of the other subgraphs, a method for computing the source to terminal reliability is proposed. the time complexity for computing all the logic product terms of one subgraph is the product of copies of the number of edges in the subgraph of 2, and that of the other subgraph is the number of edges multiplied by the number of logic product terms. This method requires less computation time than that not by decomposition.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.556-564
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• 2003

A Star and Pancake graph also have such a good property of a hypercube and have a low network cost than the hypercube. A Macro-star graph which has the star graph as a basic module has the node symmetry, the maximum fault tolerance, and the hierarchical decomposition property. And, it is an interconnection network which improves the network cost against the Star graph. In this paper, we propose a method to embed between Star graph, Pancake graph, and Macro-star graph using the edge definition of graphs. We prove that the Star graph $S_n$ can be embedded into Pancake graph $P_n$ with dilation 4, and Macro-star graph MS(2,n) can be embedded into Pancake graph $P_{2n＋1}$ with dilation 4. Also, we have a result that the embedding cost, a Pancake graph can be embedded into Star and Macro-star graph, is O(n).

• Proceedings of the Korea Society for Simulation Conference
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• 2003.06a
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• pp.73-78
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• 2003

This paper proposes the simulator synthesis scheme which is based on the exploration of the total design space in attributed AND-OR graph. Attributed AND-OR graph is a systematic design space representation formalism which enables to represent all the design space by decomposition rule and specialization rule. In addition, attributes attached to the design entity provides flexible modeling. Based on this design space representation scheme, a pruning algorithm which can transform the total design space into sub-design space that satisfies the user requirements is given. We have shown the effectiveness of our framework by (ⅰ) constructing the design space of superscalar processor in attributed AND-OR graph (ⅱ) pruning it to obtain the ARM9 processor architecture. (ⅲ) modeling the components of the architecture and (ⅳ) simulating the ARM9 model.