• 대한수학회논문집
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• 제15권3호
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• pp.521-531
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• 2000

Graph C*-algebras C*(E) are the universal C*-algebras generated by partial isometries satisfying the Cuntz-Krieger relations determined by directed graphs E, and it is known that a simple graph C*-algebra is extremally rich in sense that it contains enough extreme consider a sufficient condition on a graph for which the associated graph algebra(possibly nonsimple) is extremally rich. We also present examples of nonextremally rich prime graph C*-algebras with finitely many ideals and with real rank zero.

• 대한수학회보
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• 제59권1호
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• pp.203-212
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• 2022

A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order 12p³ for any prime number p.

• 대한수학회논문집
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• 제38권3호
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• pp.937-941
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• 2023

For each positive integer n, a square congruence graph S(n) is the graph with vertex set H = {1, 2, 3,...., n} and two vertices a, b are adjacent if they are distinct and a² ≡ b² (mod n). In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with p vertices or 2p vertices for any prime number p.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• 한국정보과학회논문지:데이타베이스
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• 제35권2호
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• pp.112-124
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• 2008

RDF와 OWL은 시맨틱 웹을 위한 두 가지 핵심 기반 기술이다. 이러한 RDF와 OWL을 이용하는, 또한 이에 관련된 많은 연구들이 최근 소개되었다. 하지만, RDF와 OWL에 대한 정보 보안 관련 연구는 미비한 실정이다. 본 논문에서는 RDF 보안 기술과 관련하여, RDF 트리플에 기반을 둔 안전한 접근제어 명세 모델을 간단히 소개한다. 다음으로 RDF 접근 제어 명세 시의 추론에 의한 권한 충돌을 효율적으로 발견하기 위하여 소수 그래프 레이블링을 기법을 활용하는 방법을 자세히 소개한다. 추론에 의한 접근 권한 충돌 문제는 비록 하위 개념에 대한 접근 권한이 허용이지만, 하위 개념은 상위 개념으로 추론될 수 있으므로, 만약 상위 개념에 대한 접근 권한이 불허로 되어 있는 경우 하위 개념 또한 허용되어서는 안 되는 문제이다. 몇 가지 실험에서는 제안하는 소수 그래프 레이블링을 사용하는 방법이 기존의 단순한 권한 충돌 발견 방법보다 현저히 나은 성능을 가짐을 보여 준다.

• 대한수학회논문집
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• 제28권1호
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• pp.79-85
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• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

• 대한수학회보
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• 제52권6호
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• pp.2025-2034
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• 2015

In this paper, we characterize some PGL(2, q) by their orders and maximum element orders. We also prove that PSL(2, p) with $p{\geqslant}3$ a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if $q=p^n$ with p a prime and n > 1, PGL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.

• 한국컴퓨터정보학회논문지
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• 제18권11호
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• pp.159-165
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• 2013

본 논문은 NP-완전 문제인 간선 색칠과 그래프 부류 결정 문제를 동시에 해결하는 O(E)의 다항시간 알고리즘을 제안하였다. 제안된 알고리즘은 최대차수-최소차수 정점 쌍 간선을 단순히 선택하는 방법으로 간선 채색수 ${\chi}^{\prime}(G)$를 결정하였다. 결정된 ${\chi}^{\prime}(G)$는 ${\Delta}(G)$ 또는 ${\Delta}(G)+1$을 얻는다. 결국, 알고리즘 수행 결과 얻은 ${\chi}^{\prime}(G)$로부터 ${\chi}^{\prime}(G)={\Delta}(G)$이면 부류 1, ${\chi}^{\prime}(G)={\Delta}(G)+1$이면 부류 2로 분류할 수 있다. 또한, 미해결 문제로 알려진 "최대차수가 6인 단순, 평면 그래프는 부류 1이다."라는 Vizing의 평면 그래프 추정도 증명하였다.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.41-46
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• 2016

A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, $2{\cdots}$, n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm ${\bar{H}}_n$, and present a new way of prime cordial labeling of $P^2_n$. Finally we make a correction of the proof of Theorem 2.5 in [12].

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.245-258
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• 2005

In this paper we prove that the alternating groups A_n, for n = p, p+1, p+2 and symmetric groups $S_n$, for n = p, p+1, where p$\ge$3 is a prime number, can be uniquely determined by their order components. As one of the important consequence of this characterization we show that the simple groups An, where n = p, p+1, P+2 and p$\ge$3 is prime, satisfy in Thompson's conjecture and Shi's conjecture.