• 호남수학학술지
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• 제38권1호
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• pp.71-84
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• 2016

The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.

• 대한수학회보
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• 제44권4호
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• pp.651-661
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• 2007

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s{\approx}t$ if the corresponding graph algebra $\underline{A(G)}$ satisfies $s{\approx}t$. A graph G=(V,E) is called an $(xy)x{\approx}x(yy)$ graph if the graph algebra $\underline{A(G)}$ satisfies the equation $(xy)x{\approx}x(yy)$. An identity $s{\approx}t$ of terms s and t of any type ${\tau}$ is called a hyperidentity of an algebra $\underline{A}$ if whenever the operation symbols occurring in s and t are replaced by any term operations of $\underline{A}$ of the appropriate arity, the resulting identities hold in $\underline{A}$. In this paper we characterize $(xy)x{\approx}x(yy)$ graph algebras, identities and hyperidentities in $(xy)x{\approx}x(yy)$ graph algebras.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• Journal of Information Processing Systems
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• 제19권6호
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• pp.803-816
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• 2023

Explainable artificial intelligence is a method that explains how a complex model (e.g., a deep neural network) yields its output from a given input. Recently, graph-type data have been widely used in various fields, and diverse graph neural networks (GNNs) have been developed for graph-type data. However, methods to explain the behavior of GNNs have not been studied much, and only a limited understanding of GNNs is currently available. Therefore, in this paper, we propose an explanation method for node classification using graph convolutional networks (GCNs), which is a representative type of GNN. The proposed method finds out which features of each node have the greatest influence on the classification of that node using GCN. The proposed method identifies influential features by backtracking the layers of the GCN from the output layer to the input layer using the gradients. The experimental results on both synthetic and real datasets demonstrate that the proposed explanation method accurately identifies the features of each node that have the greatest influence on its classification.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.623-626
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• 2000

The purpose of this paper is to find an efficient solution for multiple constant multiplication (MCM) problem. Since the circuit structure can be represented as a directed acyclic graph, evolutionary computing is considered as an effective tool for optimization of circuit synthesis. In this paper, we propose a stack type operator as a chromosome element to synthesize a directed acyclic graph efficiently. This type of chromosome can represent a graph structure with a set of simple symbols and so we can employ the similar method to a conventional GA.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1307-1318
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• 2009

An infinite locally finite plane graph is an LV-graph if it is 3-connected and VAP-free. In this paper, as a preparatory work for solving the problem concerning the existence of a spanning 3-tree in an LV-graph, we investigate the existence of a spanning 3-forest in a bridge of type 0,1 or 2 of a tight semi ring in an LV-graph satisfying certain conditions.

• 한국과학교육학회지
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• 제27권4호
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• pp.285-296
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• 2007

본 연구에서는 지구과학 그래프 유형을 분석하기 위한 기준을 만들고, 과학 교과서 비교 분석을 통하여 지구과학 그래프의 유형과 특징을 파악함으로써 지구과학 교과서에서 그래프의 기능과 구조에 대한 시사점을 얻고자 하였다. 지구과학 교과서 분석 결과, 선 그래프와 등치선도가 많이 사용되고 있는 것으로 나타났다. 선 그래프 중에는 단순 선 그래프 이외에도 다중 선 그래프와 YX 그래프의 사용 비율이 특히 높았다. 다른 과학 교과의 그래프와 비교 분석한 결과, 지구과학 교과는 다른 과학 교과에 비해 사용되는 그래프의 수가 많고 그 유형이 다양함을 알 수 있었다. 특히, 다른 과학 교과에 비해 선 그래프의 비율은 낮은 반면 등치선도, 분산 그래프 등의 비율이 높았다. 선 그래프 중에서는 특히 YX 그래프의 비율이 다른 교과에 비해 매우 높아 지구과학 교과의 가장 특정적인 그래프인 것으로 나타났다. 본 연구의 결과는 지구과학 교과서에서 그래프의 구조와 기능면에서의 개선을 시사하며, 학생들의 그래프 해석 능력에 대한 후속 연구를 제안한다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2008년도 추계학술대회 논문집
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• pp.551-552
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• 2008

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.314-318
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• 2001

Constructing a shortest path on a graph is a fundamental problem in the area of graph theory. In an application where we cannot exactly determine the weights of edges, fuzzy weights can be used instead of crisp weights, and Type-2 fuzzy weights will be more suitable if this uncertainty varies under some conditions. In this paper, shortest path problem in type-1 fuzzy weighted graphs is extended for type-2 fuzzy weighted graphes. A solution is also given based on possibility theory and extension principle.