• 대한수학회논문집
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• 제38권3호
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• pp.733-740
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• 2023

Let R be a commutative ring and M be an R-module. The dimension graph of M, denoted by DG(M), is a simple undirected graph whose vertex set is Z(M) ⧵ Ann(M) and two distinct vertices x and y are adjacent if and only if dim M/(x, y)M = min{dim M/xM, dim M/yM}. It is shown that DG(M) is a disconnected graph if and only if (i) Ass(M) = {𝖕, 𝖖}, Z(M) = 𝖕 ∪ 𝖖 and Ann(M) = 𝖕 ∩ 𝖖. (ii) dim M = dim R/𝖕 = dim R/𝖖. (iii) dim M/xM = dim M for all x ∈ Z(M) ⧵ Ann(M). Furthermore, it is shown that diam(DG(M)) ≤ 2 and gr(DG(M)) = 3, whenever M is Noetherian with |Z(M) ⧵ Ann(M)| ≥ 3 and DG(M) is a connected graph.

• 대한수학회지
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• 제42권6호
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• pp.1251-1264
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• 2005

Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u, x) and (v, x) are arcs of D. The competition number of a graph G, denoted by k(G), is the smallest number k such that G together with k isolated vertices is the competition graph of an acyclic digraph. It is known to be difficult to compute the competition number of a graph in general. Even characterizing the graphs with competition number one looks hard. In this paper, we continue the work done by Cho and Kim[3] to characterize the graphs with one hole and competition number one. We give a sufficient condition for a graph with one hole to have competition number one. This generates a huge class of graphs with one hole and competition number one. Then we completely characterize the graphs with one hole and competition number one that do not have a vertex adjacent to all the vertices of the hole. Also we show that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial, and this allows us to construct infinitely many graph having the same competition number. Finally we pose an interesting open problem.

• 대한수학회논문집
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• 제11권1호
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• pp.1-21
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• 1996

In this paper the existence of spanning 3-trees in every 3-connected locally finite vertex-accumulation-point-free planer graph is verified, which is an extension of D. Barnette to infinite graphs and which improves the result of the author.

• 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.

• 한국정보과학회논문지:데이타베이스
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• 제27권2호
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• pp.185-198
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• 2000

최근 폭발적인 증가를 보이고 있는 멀티미디어 자료의 양과 그 자료들을 이용할 수 있는 하드웨어의 발전은 멀티미디어 상연물을 이용하는 여러 응용 분야에 대한 관심을 촉발시키고 있다. 이에 멀티미디어 상연물의 효과적인 이용을 위해서는 멀티미디어 상연물과 DBMS와의 통합이 필요하다. 이 논문에서는 내용(content)에 근거한 상연물 검색과 검색 처리 기술의 문제를 다룬다. 현재 멀티미디어 상연물 제작 도구(authoring tool)들은 멀티미디어 상연물을 상연 그래프(presentation graph)를 이용하여 표현하고 있으며 상연 그래프는 DAG(directed acyclic graph)이다. 각 노드는 같은 타입의 미디어 스트림을 나타내며 에지는 스트림간의 상연 순서와 동기화 (synchronization) 방법을 나타낸다. 각각의 스트럼에 포함된 정보, 이 정보들간의 순서, 그리고 스트럼간의 상연 순서는 상연의 내용을 구성한다. GCalculus/S(GCalculus with Set Operators)는 calculus에 바탕을 둔 검색언어이며 멀티미디어 자료들의 물리적 특정과 내용을 다룰 수 있다. 개개의 노드 안에서의 정보의 변화와 노드 사이의 순서는 시간 연산자(temporal operator) Next, Connected, Until을 이용하여 표현한다. 검색의 처리를 위하여 객체 대수(object algebra)인 O-Algebra를 확장한다.

• 대한수학회보
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• 제46권6호
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.77-83
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• 2024

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (C_n × P₂) + K₁ graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

• 컴퓨터교육학회논문지
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• 제6권4호
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• pp.61-69
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• 2003

선로그래프[6]는 철도 네트워크의 선로배정 문제를 표현하는 자료구조로써 내부선분과 외부선분의 개념을 갖는 연결그래프 구조이다. 선로그래프는 일반 그래프로는 나타낼 수 없는 철도 네트워크의 선로 연결방향을 표현할 수 있지만 여전히 직교 교차선로를 일관되게 표현하지는 못한다. 이 논문에서는 가상선분 개념을 도입해서 선로그래프를 확장함으로써 직교 교차선로를 포함하는 철도 네트워크의 모든 선로연결 구조를 일관되게 표현할 수 있는 방법을 설명하고, 확장된 선로그래프인 ERG(Extended Railway Graph)의 자료구조 표현방법과 경로배정 방법을 제안한다.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2017년도 춘계학술대회
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• pp.321-324
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• 2017

버블정렬 그래프는 자료를 정렬하는 버블정렬 기법을 수학적 모델인 그래프로 모델링한 것이다. 버블정렬 그래프 Bn는 분지수 n, 라우팅 경로 길이 ${\frac{n(n-1)}{2}}$, 망비용 $O(n^3)$이다. 본 연구에서는 버블정렬 그래프의 망비용을 개선하기 위한 방법으로 버블정렬 그래프의 분지수 개수를 대략 ${\frac{1}{2}}$ 정도 줄인 제약조건을 제시한다. 이러한 제약 조건을 갖는 버블정렬 그래프는 임의의 노드 U에서 V까지 라우팅을 위해 연결된 그래프임을 증명한다.