• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.95-111
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• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.130.2-130.2
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• 2012

태양의 활동영역에서 관측할 수 있는 흑점은 주로 흑점군으로 관측되며, 태양폭발현상의 발생을 예보하기 위한 중요한 관측 대상 중 하나이다. 현재 태양 폭발을 예보하는 모델들은 McIntosh 흑점군 분류법을 사용하며 통계적 모델과 기계학습 모델로 나누어진다. 컴퓨터는 흑점군의 형태학적 특성을 연속적인 값으로 계산하지만 흑점군의 형태적 다양성으로 인해 McIntosh 분류를 잘못 분류할 수도 있다. 이러한 이유로 컴퓨터가 계산한 흑점군의 형태학적인 특성을 예보에 직접 적용하는 것이 필요하다. 우리는 흑점군의 형태학적인 특성(개수, 면적, 면적비 등)과 함께 모든 흑점을 정점(Vertex)으로 하고 그 사이를 연결하는 간선(Edge)으로 하는 간선의 거리 합이 최소인 최소신장트리(Minimum spanning tree : MST)를 작성하였다. 이 최소신장트리를 사용하여 흑점군을 검출하고 가장 면적이 큰 정점을 중심으로 트리의 깊이(Depth)와 차수(Degree)를 계산하였다. 이 방법을 2003년 SOHO/MDI의 태양 가시광 영상에 적용하여 구한 흑점군의 내부 흑점수와 면적은 NOAA에서 산출한 값들과 90%, 99%의 좋은 상관관계를 가졌다. 우리는 이 연구를 통해 흑점군의 형태학적인 특성과 더불어 예보에 직접적으로 활용할 수 있는 방법을 논의하고자 한다.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.11-17
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• 1999

A three dimensional finite element generation code has been developed attaching simple blocks. Block can be either a quadrature or a cube depending on the dimension of a subject considered. Finite element serendipity basis functions are employed to map elements between the computational domain and the physical domain. Elements can be generated with wser defined progressive ratio for each block. For blocks to be connected properly, a block should have a consistent numbering scheme for vertices, side nodes, edges and surfaces. In addition the edge information such as the number of elements and the progressive ratio for each direction should also be checked for interfaces to have unique node numbers. Having done so, user can add blocks with little worry about the orientation of blocks, Since the present the present code has been written by a Visual Basic language, it can be developed easily for a user interactive manner under a Windows environment.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.177-188
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• 2019

Suppose G is a molecular graph with edge set E(G). The hyper-Zagreb index of G is defined as $HM(G)={\sum}_{uv{\in}E(G)}[deg_G(u)+deg_G(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, all chemical trees of order $n{\geq}12$ with the first twenty smallest hyper-Zagreb index are characterized.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.205-225
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• 2022

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSO_α for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.55-67
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• 2023

In this paper we obtain a new structure of a k-annihilating ideal hypergraph of a reduced ring R, by determine the order and size of a hypergraph 𝒜𝒢_k(R). Also we describe and count the degree of every nontrivial ideal of a ring R containing in vertex set 𝒜(R, k) of a hypergraph 𝒜𝒢_k(R). Furthermore, we prove the diameter of 𝒜𝒢_k(R) must be less than or equal to 2. Finally, we determine the minimal dominating set of a k-annihilating ideal hypergraph of a ring R.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.263-271
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• 2024

A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k-choosable if any list L of admissible colors on V (G) of size k allows an injective coloring 𝜑 such that 𝜑(v) ∈ L(v) whenever v ∈ V (G). The least k for which G is injectively k-choosable is denoted by χ^l_i(G). For a planar graph G, Bu et al. proved that χ^l_i(G) ≤ ∆ + 6 if girth g ≥ 5 and maximum degree ∆(G) ≥ 8. In this paper, we improve this result by showing that χ^l_i(G) ≤ ∆ + 6 for g ≥ 5 and arbitrary ∆(G).

• Journal of the Korea Society of Computer and Information
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• v.18 no.5
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• pp.113-120
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• 2013

This paper proposes an algorithm that proves an NP-complete 4-color theorem by employing a linear time complexity where $O(n)$. The proposed algorithm accurately halves the vertex set V of the graph $G=(V_1,E_1)$ into the Maximum Independent Set (MIS) $\bar{C_1}$ and the Minimum Vertex Cover Set $C_1$. It then assigns the first color to $\bar{C_1}$ and the second to $\bar{C_2}$, which, along with $C_2$, is halved from the connected graph $G=(V_2,E_2)$, a reduced set of the remaining vertices. Subsequently, the third color is assigned to $\bar{C_3}$, which, along with $C_3$, is halved from the connected graph $G=(V_3,E_3)$, a further reduced set of the remaining vertices. Lastly, denoting $C_3$ as $\bar{C_4}$, the algorithm assigns the forth color to $\bar{C_4}$. The algorithm has successfully obtained the chromatic number ${\chi}(G)=4$ with 100% probability, when applied to two actual map and two planar graphs. The proposed "four color algorithm", therefore, could be employed as a general algorithm to determine four-color for planar graphs.

• The Journal of Korean Academy of Prosthodontics
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• v.34 no.3
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• pp.464-474
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• 1996

A principal advantage of a plastic tooth over a porcelain tooth should be its ability to bond to the denture base material. But plastic teeth could craze and wear easily, so more abrasion resistant plastic denture teeth have been developed. To resist abrasion, the degree of cross-linking was increased, but bonding to denture base meterial became more difficult. The purpose of this study was to evaluate the bond strength of plastic teeth and abrasion resistant teeth bonded to heat-curing, self-curing and light-curing denture base material. Denture tooth molds were chosen that had a>8mm diameter. The denture teeth was bonded to three denture base materials and then machined to the same dimensions. Three denture base materials were used as control groups. Prior to tensile testing, the specimens were thermocycled between $5^{\circ}C\;and\;55^{\circ}C$ for 1000cycles. Tensile testing was performed on an Instron Universal testing mechine. Experimental group ; plastic teeth(Justi Imperial)+heat-curing resin(Lucitone 199) plastic teeth(Justi Imperial)+light-curing resin(Triad) plastic teeth(Justi Imperial)+self-curing resin(Vertex SC) abrasion resistant teeth(IPN)+heat-curing resin(Lucitone 199) abrasion resistant teeth(IPN)+light-curing resin(Triad) abrasion resistant teeth(IPN)+self-curing resin(Vertex SC) Control group ; heat-curing resin(Lucitone 199) light-curing resin (Triad) self-curing resin(Vertex SC). The results were as follows : 1. The denture teeth bonded to heat-curing resin showed the cohesive failure and those bonded to the other resins showed adhesive failure. 2. Tensile bond strength of the plastic teeth bonded to self-curing resin was not significantly greater than bonded to light-curing resin(p>0.05). 3. Tensile bond strength of the abrasion resistant teeth bonded to self-curing resin was not significantly greater than bonded to light-curing resin(p>0.05). 4. Tensile bond strength of the plastic teeth to self-curing resin was not significantly different from that of the abrasion-resistant teeth(p>0.05). 5. Tensile bond strength of the plastic teeth to light-curing resin was significantly greater than that of the abrasion resistant teeth(p<0.01).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.8
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• pp.37-45
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• 2002

A two-dimensional unsteady, inviscid flow solver has been developed for the simulation of airfoil-vortex interactions on unstructured dynamically adapted meshes. The Euler solver is based on a second-order accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with the Roe's flux-difference splitting. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of both spatial and temporal variations of the flow field. The effect of vortex interaction on the aeroelastic displacement of an airfoil attached to the idealized two degree-of-freedom spring system is investigated.