• Honam Mathematical Journal
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• v.41 no.1
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• pp.67-87
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• 2019

The main aim of this study is to characterize new classes of multicone graphs which are determined by their adjacency spectra, their Laplacian spectra, their complement with respect to signless Laplacian spectra and their complement with respect to their adjacency spectra. A multicone graph is defined to be the join of a clique and a regular graph. If n is a positive integer, a friendship graph $F_n$ consists of n edge-disjoint triangles that all of them meet in one vertex. It is proved that any connected graph cospectral to a multicone graph $F_n{\nabla}F_n=K_2{\nabla}nK_2{\nabla}nK_2$ is determined by its adjacency spectra as well as its Laplacian spectra. In addition, we show that if $n{\neq}2$, the complement of these graphs are determined by their adjacency spectra. At the end of the paper, it is proved that multicone graphs $F_n{\nabla}F_n=K_2{\nabla}nK_2{\nabla}nK_2$ are determined by their signless Laplacian spectra and also we prove that any graph cospectral to one of multicone graphs $F_n{\nabla}F_n$ is perfect.

• 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.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• 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.

• 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.

• Korean Journal of Remote Sensing
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• v.27 no.6
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• pp.717-728
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• 2011

An efficient method for the unsupervised classification of high resolution imagery is suggested in this paper. It employs pixel-linking and merging based on the adjacency graph. The proposed algorithm uses the neighbor lines of 8 directions to include information in spatial proximity. Two approaches are suggested to employ neighbor lines in the linking. One is to compute the dissimilarity measure for the pixel-linking using information from the best lines with the smallest non. The other is to select the best directions for the dissimilarity measure by comparing the non-homogeneity of each line in the same direction of two adjacent pixels. The resultant partition of pixel-linking is segmented and classified by the merging based on the regional and spectral adjacency graphs. This study performed extensive experiments using simulation data and a real high resolution data of IKONOS. The experimental results show that the new approach proposed in this study is quite effective to provide segments of high quality for object-based analysis and proper land-cover map for high resolution imagery of urban area.

• 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.

• International conference on construction engineering and project management
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• 2024.07a
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• pp.351-358
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• 2024

In Japan, bridge inspections are mandated every five years. The inspection database for bridges under the jurisdiction of the Ministry of Land, Infrastructure, Transport, and Tourism enables the acquisition of damage progression data for each structural element. This study develops a methodology for predicting the deterioration of girder bridges, employing a novel approach where inspection drawings are processed using Optical Character Recognition (OCR) to extract element numbers and their spatial relationships, subsequently creating a comprehensive graph of these elements. A key feature of this prediction methodology is its ability to consider the adjacency relationships between different bridge members, made possible by the detailed analysis of drawing information and a Graph Transformer model. The research examines and compares the accuracy of predictions made with and without considering adjacency relationships, highlighting the effectiveness of incorporating detailed structural information in the predictive analysis of bridge deterioration.

• 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.

• Korean Journal of Remote Sensing
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• v.18 no.2
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• pp.107-116
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• 2002

A hybrid image segmentation algorithm is proposed which integrates edge-based and region-based techniques through the watershed algorithm. First, by using mean curvature diffusion coupled to min/max flow, noise is eliminated and thin edges are preserved. After images are segmented by watershed algorithm, the segmented regions are combined with neighbor regions. Region adjacency graph (RAG) is employed to analyze the relationship among the segmented regions. The graph nodes and edge costs in RAG correspond to segmented regions and dissimilarities between two adjacent regions respectively. After the most similar pair of regions is determined by searching minimum cost RAG edge, regions are merged and the RAG is updated. The proposed method efficiently reduces noise and provides one-pixel wide, closed contours.