• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.497-505
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• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• Journal of Broadcast Engineering
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• v.22 no.3
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• pp.366-374
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• 2017

Since a display device such as TV or digital signage is getting larger, the types of media is getting changed into wider view one such as UHD, panoramic and jigsaw-like media. Especially, panoramic and jigsaw-like media is realized by stitching video clips, which are captured by different camera or devices. However, a stitching process takes long time, and has difficulties in applying for a real-time process. Thus, this paper suggests to find out 2D Adjacency Matrix, which tells spatial relationships among those video clips in order to decrease a stitching processing time. Using the Discrete Cosine Transform (DCT), we convert the each frame of video source from the spatial domain (2D) into frequency domain. Based on the aforementioned features, 2D Adjacency Matrix of images could be found that we can efficiently make the spatial map of the images by using DCT. This paper proposes a new method of generating 2D adjacency matrix by using DCT for producing a panoramic and jigsaw-like media through various individual video clips.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2016.11a
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• pp.39-42
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• 2016

Since a display device such as TV or signage is getting larger, the types of media is getting changed into wider view one such as UHD, panoramic and jigsaw-like media. Especially, panoramic and jigsaw-like media is realized by stitching video clips, which are captured by different camera or devices. In order to stich those video clips, it is required to find out 2D Adjacency Matrix, which tells spatial relationships among those video clips. Discrete Cosine Transform (DCT), which is used as a compression transform method, can convert the each frame of video source from the spatial domain (2D) into frequency domain. Based on the aforementioned compressed features, 2D adjacency Matrix of images could be found that we can efficiently make the spatial map of the images by using DCT. This paper proposes a new method of generating 2D adjacency matrix by using DCT for producing a panoramic and jigsaw-like media through various individual video clips.

• Journal of the Korean Data and Information Science Society
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• v.25 no.5
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• pp.1107-1116
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• 2014

In this paper, we review recent developments in network analysis using the graph theory, and introduce ongoing research area with relevant theoretical results. In specific, we introduce basic notations in graph, and conditional and marginal approach in constructing the adjacency matrix. Also, we introduce the Marcenko-Pastur law, the Tracy-Widom law, the white Wishart distribution, and the spiked distribution. Finally, we mention the relationship between degrees and eigenvalues for the detection of hubs in a network.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.215-224
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• 2006

We call the bipartite graph G is normal provided the reduced adjacency matrix A of G is normal. In this paper we give graph representations of normal matrices. In addition we shall have the characterization of signed bipartite normal graphs.

• 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.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1116-1120
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• 1987

In this paper, the Adjacency Matrix is applied to analyze the MIN, which is one of the kind and further implemented in designing the new kind of SSIN, which provides the special form of MIN that has identical link patterns between switching stages. At first, new theorems are established and next the classes of the SSIN are generated from computer simulation.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.75-86
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• 1996

Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.103-110
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• 2005

This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.127-134
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• 1979

A (0,1) matrix is acyclic if it does not have a permutation matrix of order 2 as a submatrix. A bipartite tournament is acyclic if and only if its adjacency matrix is acyclic. The concepts of (maximal) order of cyclicity of a matrix and a bipartite tournament are introduced and studied.