• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.227-248
• /
• 2017

In this paper, we reduce the classification problem of equivariant (topological complex) vector bundles over a simple graph to the classification problem of their isotropy representations at vertices and midpoints of edges. Then, we solve the reduced problem in the case when the simple graph is homeomorphic to a circle. So, the paper could be considered as a generalization of [3].

• Journal of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1515-1528
• /
• 2019

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

• Journal of the Korean Mathematical Society
• /
• v.60 no.6
• /
• pp.1171-1213
• /
• 2023

This work is a continuation of Crisp's work on automorphism groups of CLTTF Artin groups, where the defining graph of a CLTTF Artin group is connected, large-type, and triangle-free. More precisely, we provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group whose defining graph has no separating vertices.

• Journal of Intelligence and Information Systems
• /
• v.27 no.4
• /
• pp.49-71
• /
• 2021

Users who intend to utilize knowledge to actively solve given problems proceed their jobs with cross- and sequential exploration of associated knowledge related each other in terms of certain criteria, such as content relevance. A knowledge map is the diagram or taxonomy overviewing status of currently managed knowledge in a knowledge-base, and supports users' knowledge exploration based on certain relationships between knowledge. A knowledge map, therefore, must be expressed in a networked form by linking related knowledge based on certain types of relationships, and should be implemented by deploying proper technologies or tools specialized in defining and inferring them. To meet this end, this study suggests a methodology for developing the knowledge graph-based knowledge map using the Graph DB known to exhibit proper functionality in expressing and inferring relationships between entities and their relationships stored in a knowledge-base. Procedures of the proposed methodology are modeling graph data, creating nodes, properties, relationships, and composing knowledge networks by combining identified links between knowledge. Among various Graph DBs, the Neo4j is used in this study for its high credibility and applicability through wide and various application cases. To examine the validity of the proposed methodology, a knowledge graph-based knowledge map is implemented deploying the Graph DB, and a performance comparison test is performed, by applying previous research's data to check whether this study's knowledge map can yield the same level of performance as the previous one did. Previous research's case is concerned with building a process-based knowledge map using the ontology technology, which identifies links between related knowledge based on the sequences of tasks producing or being activated by knowledge. In other words, since a task not only is activated by knowledge as an input but also produces knowledge as an output, input and output knowledge are linked as a flow by the task. Also since a business process is composed of affiliated tasks to fulfill the purpose of the process, the knowledge networks within a business process can be concluded by the sequences of the tasks composing the process. Therefore, using the Neo4j, considered process, task, and knowledge as well as the relationships among them are defined as nodes and relationships so that knowledge links can be identified based on the sequences of tasks. The resultant knowledge network by aggregating identified knowledge links is the knowledge map equipping functionality as a knowledge graph, and therefore its performance needs to be tested whether it meets the level of previous research's validation results. The performance test examines two aspects, the correctness of knowledge links and the possibility of inferring new types of knowledge: the former is examined using 7 questions, and the latter is checked by extracting two new-typed knowledge. As a result, the knowledge map constructed through the proposed methodology has showed the same level of performance as the previous one, and processed knowledge definition as well as knowledge relationship inference in a more efficient manner. Furthermore, comparing to the previous research's ontology-based approach, this study's Graph DB-based approach has also showed more beneficial functionality in intensively managing only the knowledge of interest, dynamically defining knowledge and relationships by reflecting various meanings from situations to purposes, agilely inferring knowledge and relationships through Cypher-based query, and easily creating a new relationship by aggregating existing ones, etc. This study's artifacts can be applied to implement the user-friendly function of knowledge exploration reflecting user's cognitive process toward associated knowledge, and can further underpin the development of an intelligent knowledge-base expanding autonomously through the discovery of new knowledge and their relationships by inference. This study, moreover than these, has an instant effect on implementing the networked knowledge map essential to satisfying contemporary users eagerly excavating the way to find proper knowledge to use.

• Journal of applied mathematics & informatics
• /
• v.33 no.1_2
• /
• pp.101-110
• /
• 2015

A Total Mean Cordial labeling of a graph G = (V, E) is a function $f:V(G){\rightarrow}\{0,1,2\}$ such that $f(xy)={\Large\lceil}\frac{f(x)+f(y)}{2}{\Large\rceil}$ where $x,y{\in}V(G)$, $xy{\in}E(G)$, and the total number of 0, 1 and 2 are balanced. That is ${\mid}ev_f(i)-ev_f(j){\mid}{\leq}1$, $i,j{\in}\{0,1,2\}$ where $ev_f(x)$ denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there is a total mean cordial labeling on a graph G, then we will call G is Total Mean Cordial. Here, We investigate the Total Mean Cordial labeling behaviour of prism, gear, helms.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.335-340
• /
• 2019

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is defined for the Laplacian matrix, Distance matrix, Commonneighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which $ij^{th}$ entry is -1 or 1, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is 0, if $v_i=v_j$. The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have different eigenvalues, but who have the same Seidel energies.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2018.10a
• /
• pp.984-987
• /
• 2018

In an Internet of Thing (IoT) environment, entities with different attributes and capacities are going to be connected in a highly connected fashion. Specifically, not only the mechanical and electronic devices but also other entities such as people, locations and applications are connected to each other. Understanding and managing these connections play an important role for businesses, which identify opportunities for new IoT services. Traditional approach for storing and querying IoT data is used of a relational database management system (RDMS) such as MySQL or MSSQL. However, using RDMS is not flexible and sufficient for handling heterogeneous IoT data because these data have deeply complex relationships which require nested queries and complex joins on multiple tables. In this paper, we propose a graph model for constructing a graph database of heterogeneous IoT data. Graph databases are purposely-built to store highly connected data with nodes representing entities and edges representing the relationships between these entities. Our model fuses social graph, spatial graph, and things graph, and incorporates the relationships among them. We then present a case study which applies our model for representing data from a Smart Campus using Neo4J platform. Through the results of querying to answer real questions in Smart Campus management, we show the viability of our model.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1623-1634
• /
• 2008

The complete multipartite graph $K_{n(2t)}$ having n partite sets of size 2t, with $n\;{\geq}\;6$ and $t\;{\geq}\;1$, is shown to have a decomposition into gregarious 6-cycles, that is, the cycles which have at most one vertex from any particular partite set. Complete sets of differences of numbers in ${\mathbb{Z}}_n$ are used to produce starter cycles and obtain other cycles by rotating the cycles around the n-gon of the partite sets.

• Proceedings of the Korean Information Science Society Conference
• /
• 2001.10b
• /
• pp.79-81
• /
• 2001

그래프 착색 문제(Graph Coloring Problem)는 인접한 노드 (V$_{i}$, V$_{j}$ )가 같은 색을 갖지 않도록 그래프 G의 노드 V에 색을 배정하는 문제로, NP-hard 문제로 잘 알려져 있다. 또한 최근까지 그래프 착색 문제의 최적 해를 구하기 위하여 다양한 접근방식들과 해법들이 제안되고 있다. 본 논문에서는 기존의 그래프 착색 문제의 해법으로 잘 알려진 Greedy algorithms, Simulated Annealing. Tabu search 등이 아닌 실세계에서 개미들이 자신의 분비물을 이용하여 경로를 찾는 Ant System을 개선하여 새롭게 제안한 Ant Colony System(ACS) 알고리즘으로 해를 구하는 ANTCOL을 소개하고, ANTCOL에서 DSATUR, Recursive Largest First(RLF) 등의 방식을 사용한 기존 생성 함수들과 RLF를 개선하여 제안한 eXtend RLF방식을 사용한 생성 함수를 비교, 평가하고자 한다.

• Proceedings of the Korean Information Science Society Conference
• /
• 2007.10d
• /
• pp.306-311
• /
• 2007

본 논문에서는 Wireless Sensor Network상에서 전체 노드들의 lifetime을 증대시키기 위하여 "random한" 방식으로 cluster-head를 선출하는 LEACH 알고리즘이 가지고 있는 cluster-head 선출 과정에서 선출되는 수와 선출되는 노드들의 위치가 적절히 분산되지 않는 문제를 해결하기 위해 변형된 Graph Coloring 문제를 기반으로 노드의 위치 정보를 사용하지 않고 cluster-head를 적절히 분산하여 선출함으로써 효율적인 clustering을 하는 중앙처리 방식의 새로운 알고리즘 "GCCA : Graph Coloring based Clustering Algorithm for Wireless Sensor Networks" 을 제안한다. GCCA는 cluster-head가 선출되는 수를 일정하게 유지하고 선출되는 노드의 위치가 전체 network area에 적절히 분산되는 효과를 가져 옴으로 LEACH 알고리즘보다 에너지 효율이 증대됨을 실험을 통하여 보인다.