• Journal of Institute of Control, Robotics and Systems
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• v.20 no.12
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• pp.1225-1230
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• 2014

This paper investigates the group average-consensus and group formation-consensus problems for first-order multi-agent systems. The control protocol for group consensus is designed by considering the positive adjacency elements. Since each intra-group Laplacian matrix cannot be satisfied with the in-degree balance because of the positive adjacency elements between groups, we decompose the Laplacian matrix into an intra-group Laplacian matrix and an inter-group Laplacian matrix. Moreover, average matrices are used in the control protocol to analyze the stability of multi-agent systems with a fixed and undirected communication topology. Using the graph theory and the Lyapunov functional, stability analysis is performed for group average-consensus and group formation-consensus, respectively. Finally, some simulation results are presented to validate the effectiveness of the proposed control protocol for group consensus.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• The KIPS Transactions:PartC
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• v.15C no.6
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• pp.531-538
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• 2008

With the dynamic and mobile nature of ad hoc networks, links may fail due to topology changes. So, a major challenge in ad hoc network is dynamically to search paths from a source to destination with an efficient routing method, which is an important issue for delay-sensitive real-time application. The main concerns of graph theory in communications are finding connectivity and searching paths using given nodes. A topology of the nodes in ad hoc networks can be modeled as an adjacency matrix. In this paper, based on this adjacency matrix, we propose new path search algorithms using a sequence of matrix calculation. The proposed algorithms can search paths from a destination to a source using connectivity matrix. Two matrix-based algorithms for two different purposes are proposed. Matrix-Based Backward Path Search(MBBS) algorithm is designed for shortest path discovery and Matrix-Based Backward Multipath Search(MBBMS) algorithm is for multipath search.

• Journal of the Semiconductor & Display Technology
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• v.20 no.3
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• pp.113-116
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• 2021

As artificial intelligence technologies, including deep learning, develop, these technologies are being introduced to code similarity analysis. In the traditional analysis method of calculating the graph edit distance (GED) after converting the source code into a control flow graph (CFG), there are studies that calculate the GED through a trained graph neural network (GNN) with the converted CFG, Methods for analyzing code similarity through CNN by imaging CFG are also being studied. In this paper, to determine which approach will be effective and efficient in researching code similarity analysis methods using artificial intelligence in the future, code similarity is measured through funcGNN, which measures code similarity using GNN, and Siamese Network, which is an image similarity analysis model. The accuracy was compared and analyzed. As a result of the analysis, the error rate (0.0458) of the Siamese network was bigger than that of the funcGNN (0.0362).

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.2
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• pp.85-89
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• 1987

The large sparse matrix problems arise in many applications areas, such as structural analysis, network analysis. In dealing with such sparse systems proper preprogramming techniques such as permuting rows and columns simultaneously, will be needed in order to reduce the number of arithmetic operations and storage spaces.

• Korean Journal of Computational Design and Engineering
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• v.6 no.3
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• pp.174-183
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• 2001

This study proposes an improved genetic algorithm (GA) to derive solutions for facility layout problems having inner walls and passages. The proposed algorithm models the layout of facilities on a flour-segmented chromosome. Improved solutions are produced by employing genetic operations known as selection, crossover, inversion, mutation, and refinement of these genes for successive generations. All relationships between the facilities and passages are represented as an adjacency graph. The shortest path and distance between two facilities are calculated using Dijkstra's algorithm of graph theory. Comparative testing shows that the proposed algorithm performs better than other existing algorithm for the optimal facility layout design. Finally, the proposed algorithm is applied to ship compartment layout problems with the computational results compared to an actual ship compartment layout.

• Journal of Intelligence and Information Systems
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• v.2 no.1
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• pp.45-58
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• 1996

This paper describes an a, pp.oach to recognizing composite features of prismatic parts. AAG (Attribute Adjacency Graph) is adopted as the basis of describing basic feature, but it is extended to enhance the expressive power of AAG by adding face type, angles between faces and normal vectors. Our a, pp.oach is called Extended AAG (EAAG). To simplify the recognition procedure, feature classification tree is built using the graph types of EEA and the number of EAD's. Algorithms to find open faces and dimensions of features are exemplified and used in decomposing composite feature. The processing sequence of recognized features is automatically determined during the decomposition process of composite features.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.28.3-28
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• 2001

This paper proposes a new algorithm that detects and separates the occluding and occluded objects in a 2D image. An input image is represented by the attributed graph where a node corresponds to a surface and an arc connecting two nodes describes the adjacency of the nodes in the image. Each end of arc is weighted by relation value which tells the number of edges connected to the surface represented by the node in the opposite side of the arc. In attributed graph homogeneous nodes pertained to the same object always construct one of three special patterns which can be simply classified by comparison of relation values of the arcs. The experimental results have shown that the proposed algorithm efficiently separates the objects ...

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.335-340
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• 2019

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is defined for the Laplacian matrix, Distance matrix, Commonneighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which $ij^{th}$ entry is -1 or 1, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is 0, if $v_i=v_j$. The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have different eigenvalues, but who have the same Seidel energies.