• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.417-429
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• 2015

Let R be a commutative ring with unity. The annihilator ideal graph of R, denoted by ${\Gamma}_{Ann}(R)$, is a graph whose vertices are all non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if $I{\cap}Ann(J){\neq}\{0\}$ or $J{\cap}Ann(I){\neq}\{0\}$. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose annihilator ideal graphs are totally disconnected. Also, we study diameter, girth, clique number and chromatic number of this graph. Moreover, we study some relations between annihilator ideal graph and zero-divisor graph associated with R. Among other results, it is proved that for a Noetherian ring R if ${\Gamma}_{Ann}(R)$ is triangle free, then R is Gorenstein.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.1
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• pp.269-276
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• 2015

This paper proves the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture of the vertex coloring problem, which is so far unresolved. The Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture states that "the union of k copies of k-cliques intersecting in at most one vertex pairwise is k-chromatic." i.e., x(G)=k. In a bid to prove this conjecture, this paper employs a method in which it determines the number of intersecting vertices and that of cliques that intersect at one vertex so as to count a vertex of the minimum degree ${\delta}(G)$ in the Minimum Independent Set (MIS) if both the numbers are even and to count a vertex of the maximum degree ${\Delta}(G)$ in otherwise. As a result of this algorithm, the number of MIS obtained is x(G)=k. When applied to $K_k$-clique sum intersecting graphs wherein $3{\leq}k{\leq}8$, the proposed method has proved to be successful in obtaining x(G)=k in all of them. To conclude, the Erd$\ddot{o}$s-Faber-Lov$\acute{a}$sz conjecture implying that "the k-number of $K_k$-clique sum intersecting graph is k-chromatic" is proven.

• Journal of the Korean Institute of Landscape Architecture
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• v.50 no.5
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• pp.90-102
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• 2022

In recent years, as interest in healing increases, outdoor spaces with the concept of healing have been created. For more professional and in-depth planning and design, the perception and characteristics of outdoor healing places through social media posts were analyzed using NER. Text mining was conducted using 88,155 blog posts, and frequency analysis and clique cohesion analysis were conducted. Six elements were derived through a literature review, and two elements were added to analyze the perception and the characteristics of healing places. As a result, visitors considered place elements, date and time, social elements, and activity elements more important than personnel, psychological elements, plants and color, and form and shape when visiting healing places. The analysis allowed the derivation of perceptions and characteristics of healing places through keywords. From the results of the Clique, keywords, such as places, date and time, and relationship, were clustered, so it was possible to know where, when, what time, and with whom people were visiting places for healing. Through the study, the perception and characteristics of healing places were derived by analyzing large-scale data written by visitors. It was confirmed that specific elements could be used in planning and marketing.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.65-72
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• 1998

Many optimization problems like domination and Steiner tree are NP-complete on chordal graphs but can be solved in polyno-mial time on doubly chordal graphs. Investigating properties of dou-bly chordal graphs probably help to design efficient algorithms for the graphs. We present some characterizations of dobly chordal graphs which are based on clique matrices and neighborhood matrics also men-tioned how a doubly perfect elimination ordering of a doubly chordal graph can be computed from the results.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.175-190
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• 2019

In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1409-1418
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• 2021

In this paper, we study domination in the zero-divisor graph of a *-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two *-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart *-ring and relate it with the clique of the zero-divisor graph of a Rickart *-ring.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38B no.1
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• pp.87-96
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• 2013

Influence propagation is an important research issue in social networks. Influence propagation means that the status or the disposition of nodes get changed by new idea, information and gossip propagated by other nodes. Influenced nodes also make other nodes influenced across the network. The influence propagation problem based on 'word of mouth' referral is to find most influential nodes set in networks to maximize influence. In this paper, we study the influence measuring and finding most influential nodes set in Delay-Tolerant Networks. It is difficult to measure exact influential power in Delay-Tolerant networks where network topology is not stable due to the nodal mobility. In this paper, we propose a distributed scheme that each node constructs $k$-clique community structure and estimates local influential power in Delay-Tolerant Networks. Simulation results show that the influential nodes information estimated by proposed scheme is in agreement with a global view of influential nodes information.

• Journal of architectural history
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• v.13 no.3
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• pp.85-95
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• 2004

Through 16-17th century, Neo-Confucianism was accepted and extended to Chosun Dynasty. The architecture of the Taegae school made buildings of Yongnam area rich by adding the regional characteristics based on Taegae's thought of architecture. The following is the architectural characteristics of the academic clique around Sangju. Transformation such as separation and combination of the Jeongsa space by function, lifted floor type reflecting local feature or high platform was appeared, and the architectural characteristics of the Taegae school, that is, a small scale, a moderate figure, a type of side-attached floor, landscape, were still maintained at the same time. The characteristics of the Taegae school and regional figure of Sangju were well joined. The upper class houses, Seodang, Jeongsa and Seowon, built by Confucianist had shared common Confucian characteristics in spite of their different purposes. The world view of the Confucianism such as sacrifice for sages, cultivation, devoting for study, teaching disciples, and education for villagers was revealed through the Confucian architecture including dwelling houses during the 16-17th century. Buildings of Confucianist were focused on the space for men. Seoae and Kyumam built two different Jeongsa's inside and outside of the boundary of the nakdong river. While Seodang and Jeongsa located outside of the boundary of the river were built excluding spaces for living, the function of the Jeongsa located inside of the boundary of the river was assimilated by Sarangcahe. However, both buildings kept the function for cultivation, devoting for study and teaching.

• Journal of Digital Convergence
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• v.19 no.10
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• pp.403-410
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• 2021

Given an undirected simple graph, k-club is one of the proposed structures to model social groups that exist in various types in Social Network Analysis (SNA). Maximum k-Club Problem (MkCP) is to find a k-club of maximum cardinality in a graph. This paper introduces a Genetic Algorithm called HGA+DROP which can be used to approximate maximum k-club in graphs. Our algorithm modifies the existing k-CLIQUE & DROP algorithm and utilizes Heuristic Genetic Algorithms (HGA) to obtain multiple k-clubs. We experiment on DIMACS graphs for k = 2, 3, 4 and 5 to compare the performance of the proposed algorithm with existing algorithms.