• 호남수학학술지
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• 제41권1호
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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.

• 대한수학회보
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• 제54권2호
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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.

• 호남수학학술지
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• 제36권1호
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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].

• 대한수학회지
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• 제43권1호
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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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• 제25권5호
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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.

• 대한원격탐사학회지
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• 제27권6호
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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.

• 대한수학회보
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• 제33권1호
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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.

• 국제학술발표논문집
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• The 10th International Conference on Construction Engineering and Project Management
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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.

• 한국수학사학회지
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• 제18권1호
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• pp.103-110
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• 2005

스위스 수학자 오일러에 의하여 해결된 쾨니히스베르크의 다리문제에 대한 역사적 배경과 그 응용으로서 그래프의 컴퓨터 표현에 대하여 간단한 예를 통하여 행렬로 표현하였고 오일러 회로에 의한 행렬 표현을 연구해 보았다.

• 대한원격탐사학회지
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• 제18권2호
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• pp.107-116
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• 2002

Watershed 알고리듬을 통해 에지 기반과 영역 기반 기법을 결합한 하이브리드 영상 분할 알고리듬을 제안하였다. 먼저 minimax flow와 결합된 평균 곡률 확산을 이용하여 에지를 보존하면서 잡음을 제거를 수행한다. 영상을 watershed 알고리듬을 이용하여 분할한 후에 RAG (Region Adjacency Graph)을 사용하여 분할된 영역들간의 관계를 분석한다. RAG의 그래프 노드와 에지 비용은 분할된 영역과 두 인접한 영역사이의 상이함을 나타낸다. 최소 비용의 RAG의 에지를 찾아 가장 유사한 영역 쌍이 결정되면 두 영역은 서로 합치고 RAG은 갱신된다. 제안한 방법을 통해서 잡음을 효과적으로 감소시키고 한 화소 두께의, 닫힌 경계선을 획득할 수 있었다.