• 한국컴퓨터산업학회논문지
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• 제10권5호
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• pp.187-192
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• 2009

본 논문에서 개개인의 인증을 위한 그래프 이론을 사용한 손등 표면의 정맥 패턴의 인식을 알고리즘을 제안하였다. 개인 고유의 손 정맥 패턴의 데이터이미지를 사용하여 우리는 기대되는 응답의 측정을 위한 그래프 이론의 틀 내에서 매칭 알고리즘을 사용했다. 전처리과정을 통해 캡쳐된 이미지는 좀 더 날카롭고 명료하게 변환하였으며 세선화하였다. 세선화 후 이 이미지는 다시 정규화하여 노드와 에지셀을 갖춘 그래프를 만들었다. 이 정규화된 그래프는 인접 매트릭스를 만들 수 있었으며, 개개인의 정맥 패턴으로 부터 각각의 인접 매트릭스는 달랐다. 우리는 개인의 정맥 패턴은 실험을 통해 생체인식의 새로운 방법으로 접근할 수 있었다.

• 대한수학회논문집
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• 제11권4호
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권3호
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• pp.233-241
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• 2005

Mathematics has developed dramatically in today's world and come to be increasingly put into practical use in various fields in society. However, many Japanese students dislike mathematics. We have to study mathematics education with this situation in our mind. When we consider a better educational material, we don't have to consider only within the framework of the current school mathematics. We can expect to find good mathematical materials in fields beyond the school mathematics. In this paper, we study how the inclusion of idea such as 'fuzzy theory' and 'graph theory' influences pupils' approaches to learning mathematics.

• 한국안전학회지
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• 제13권2호
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• pp.136-144
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• 1998

FTA is the most commonly used method among quantitative safety assessment. In case that the observing system become larger, a lot of terms should be calculated to accomplish FTA through complicated process. Many methods have been tried to reduce time, one of tries is How to calculate the reliability using graph theory after changing W to graph. This paper suggests an algorithm that can calculate more rapidly reliability and outset of system expressed by non-linear graph as like as FTA or CCA.

• 대한수학회지
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• 제56권1호
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• pp.113-125
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• 2019

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

• 한국수학교육학회지시리즈A:수학교육
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• 제12권2호
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• pp.1-4
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• 1974

Matroid theory, which was first introduced in 1935 by Whitney (2), is a branch of combinational mathematics which has some very much to the fore in the last few years. H. Whitney had just spent several years working in the field of graph theory, and had noticed several similarities between the ideas of independence and rank in graph theory and those of linear independence and dimension in the study of vector spaces. A matroid is essentially a set with some kind of 'independence structure' defined on it. There are several known results concerning how matroids can be induced from given matroid by a digraph. The purpose of this note is to show that, given a matroid M$_{0}$ (N) and a digraph $\Gamma$(N), then a new matroid M(N) is induced, where A⊆N is independent in M(N) if and only if A is the set of initial vertices of a family of pairwise-vertex-disjoint paths with terminal vertices independent in M$_{0}$ (N).(N).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.19-38
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• 2007

Graph theory is becoming increasingly significant as it is applied of mathematics, science and technology. It is being actively used in fields as varied as biochemistry(genomics), electrical engineering(communication networks and coding theory), computer science(algorithms and computation) and operations research(scheduling). The powerful results in other areas of pure mathematics. Rhis paper, besides giving a general outlook of these facts, includes new graph theoretical proofs of Fermat's Little Theorem and the Nielson-Schreier Theorem. New applications to DNA sequencing (the SNP assembly problem) and computer network security (worm propagation) using minimum vertex covers in graphs are discussed. We also show how to apply edge coloring and matching in graphs for scheduling (the timetabling problem) and vertex coloring in graphs for map coloring and the assignment of frequencies in GSM mobile phone networks. Finally, we revisit the classical problem of finding re-entrant knight's tours on a chessboard using Hamiltonian circuits in graphs.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.567-582
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• 2024

A total coloring of a graph G is an assignment of colors to the elements of a graphs G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G , denoted by χ''(G), is the minimum number of colors that suffice in a total coloring. In this paper, we proved the Behzad and Vizing conjecture for certain convex polytope graphs D^p_n, Q^p_n, R^p_n, E_n, S_n, G_n, T_n, U_n, C_n,respectively. This significant result in a graph G contributes to the advancement of graph theory and combinatorics by further confirming the conjecture's applicability to specific classes of graphs. The presented proof of the Behzad and Vizing conjecture for certain convex polytope graphs not only provides theoretical insights into the structural properties of graphs but also has practical implications. Overall, this paper contributes to the advancement of graph theory and combinatorics by confirming the validity of the Behzad and Vizing conjecture in a graph G and establishing its relevance to applied problems in sciences and engineering.

• 정보교육학회논문지
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• 제20권1호
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• pp.93-100
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• 2016

언플러그드 컴퓨터과학 활동은 카드, 실, 크래용 등 주변의 물건들을 사용하는 놀이와 퍼즐을 통하여 컴퓨터과학에 대하여 학습하는 활동의 모음이다. 기존의 언플러그드 활동은 알고리즘을 소개하고 실생활에 적용하는 것에 편중되어 문제 해결을 위하여 알고리즘을 적용하기 전에 이루어져야 할 자료의 표현 방법에 대한 활동은 상대적으로 부족한 실정이다. 본 연구에서는 초등학생들에게 그래프 이론의 기본 개념과 실생활에 적용할 수 있는 그래프 알고리즘을 소개하는 언플러그드 수업을 설계하고 수업을 실시한 후에 설문조사를 통하여 수준의 적절성과 수업 효과에 대하여 평가하였다. 설문 응답을 분석한 결과 모든 응답자가 본 연구에서 제시한 수업 내용이 초등학생에게 적합하다고 응답하였고 수업의 효과와 적절성에 대하여 긍정적인 응답을 보였다.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.399-426
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• 2018

Cofinite graphs and cofinite groupoids are defined in a unified way extending the notion of cofinite group introduced by Hartley. These objects have in common an underlying structure of a directed graph endowed with a certain type of uniform structure, called a cofinite uniformity. Much of the theory of cofinite directed graphs turns out to be completely analogous to that of cofinite groups. For instance, the completion of a directed graph Γ with respect to a cofinite uniformity is a profinite directed graph and the cofinite structures on Γ determine and distinguish all the profinite directed graphs that contain Γ as a dense sub-directed graph. The completion of the underlying directed graph of a cofinite graph or cofinite groupoid is observed to often admit a natural structure of a profinite graph or profinite groupoid, respectively.