• Journal of the Korea Society of Computer and Information
• /
• v.23 no.12
• /
• pp.57-64
• /
• 2018

In this paper, a method to measure similarity between two graphs is proposed, which is based on centralities of the graphs. The similarity between two graphs $G_1$ and $G_2$ is defined by the difference of distance($G_1$, $G_{R_1}$) and distance($G_2$, $G_{R_2}$), where $G_{R_1}$ and $G_{R_2}$ are set of random graphs that have the same number of nodes and edges as $G_1$ and $G_2$, respectively. Each distance ($G_*$, $G_{R_*}$) is obtained by comparing centralities of $G_*$ and $G_{R_*}$. Through the computational experiments, we show that it is possible to compare graphs regardless of the number of vertices or edges of the graphs. Also, it is possible to identify and classify the properties of the graphs by measuring and comparing similarities between two graphs.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.671-677
• /
• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• 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 $d{\geq}2t$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2016.05a
• /
• pp.819-822
• /
• 2016

This paper proposes an algorithm recognizing finger using a distance graph of a detected finger's contour in a depth image. The distance graph shows angles and Euclidean distances between the center of palm and the hand contour as x and y axis respectively. We can obtain hand gestures from the graph using the fact that the graph has local maximum at the positions of finger tips. After we find the center of mass of the wrist using the fingers is thinner than the palm, we make its angle the orienting angle $0^{\circ}$. The simulation results show that the proposed algorithm can detect hand gestures well regardless of the hand direction.

• The Journal of the Acoustical Society of Korea
• /
• v.15 no.1
• /
• pp.54-60
• /
• 1996

In most pattern recognition and image understanding applications, images are degraded by noise and other distortions. Therefore, it is more relevant to decide how similar two objects are rather than to decide whether the two are exactly the same. In this paper, we propose a method for recognizing degraded symbols using a distance measure between two graphs representing the symbols. a symbol is represented as a graph consisting of nodes and edges based on the run graph concept. The graph is then transformed into a reference model graph with production rule containing the embedding transform. The symbols are recognized by using the distance measure which is estimated by using the number of production rules used and the structural homomorphism between a transformed graph and a model graph. the proposed approach is applies to the recognition of non-note musical symbols and the result are given.

• Journal of Korea Multimedia Society
• /
• v.19 no.12
• /
• pp.1927-1935
• /
• 2016

This paper propose a framework for human body parts in RGB-D image. We conduct tasks of obtaining person area, finding candidate areas and local detection in order to detect hand, foot and head which have features of long accumulative geodesic distance. A person area is obtained with background subtraction and noise removal by using depth image which is robust to illumination change. Finding candidate areas performs construction of graph model which allows us to measure accumulative geodesic distance for the candidates. Instead of raw depth map, our approach constructs graph model with segmented regions by quadtree structure to improve searching time for the candidates. Local detection uses HOG based SVM for each parts, and head is detected for the first time. To minimize false detections for hand and foot parts, the candidates are classified with upper or lower body using the head position and properties of geodesic distance. Then, detect hand and foot with the local detectors. We evaluate our algorithm with datasets collected Kinect v2 sensor, and our approach shows good performance for head, hand and foot detection.

• Journal of Educational Research in Mathematics
• /
• v.19 no.1
• /
• pp.123-142
• /
• 2009

Dynamic context is considered as a source for intuitive understanding on the calculus. The relation between the area under time-velocity graph and distance is the base of the dynamic contexts which are treated in the integral calculus. The fundamental theorem of calculus has originated in dynamic contexts. This paper investigated the fundamental theorem of calculus via the relation between the area under time-velocity graph and distance. And we analyzed mathematics textbooks and the understanding of students. Finally we suggest some proposal for the teaching of the fundamental theorem of calculus.

• The Transactions of the Korea Information Processing Society
• /
• v.3 no.4
• /
• pp.766-780
• /
• 1996

This paper presents a mapping scheme for parallel processing using an accurate characterization of the communication overhead. A set of objective functions is formulated to evaluate the optimality of mapping a problem graph into a system graph. One of them is especially suitable for real-time applications of parallel processing. These objective functions are different from the conventional objective functions in that the edges in the problem graph are weighted and the actual distance rather than the nominal distance for the edges in the system graph is employed. This facilitates a more accurate qualification of the communication overhead. An efficient mapping scheme has been developed for the objective functions, where two levels of assignment optimization procedures are employed: initial assignment and pairwise exchange. The mapping scheme has been tested using the hypercube as a system graph.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.119-139
• /
• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• Korean Institute of Interior Design Journal
• /
• v.18 no.4
• /
• pp.97-104
• /
• 2009

This thesis analyzed arrangement and mixture method of function elements, which are getting more important in museum planning. It used quantitative method, Space Syntax and Visibility Graph Analysis tool to analyze five case museums. Through this analysis, advantages and disadvantages of two methods were derived and case museums' arrangement and mixture attributes were grasped. Results of the analysis were derived differently by two kinds of plan form which were room to room type and open type. Open typed museum recorded similar graphs of Integration, Visual Integration and Visual Connectivity. Since whole space structures were relatively simple and structure of exhibition halls were opened, the results of Space Syntax and Visibility Graph Analysis had similar graphs. Room to room typed museum showed differences in Integration, Visual Integration and Visual Connectivity. In the result, the most accessible space was lobby and Mediation Space became the center of visibility. Also, the exhibition hall, where the opening of room to room typed exhibition hall was penetrated visually, became a center of visibility. Lobby space, which was close to entrance, had the highest Visibility Connectivity. As Space Syntax could analyze the museum as whole space structure, Space Syntax showed strength in room to room typed museum analysis compared to open typed museum analysis which has relatively simple structure. Visibility Graph Analysis could expect the flow of exhibit distance including visibility analysis unlike the flow of exhibit distance with space arrangement. The exhibition hall, which secures the sight to penetration of an opening, couldn't be analyzed in existing Space Syntax. However, it became the biggest advantages in Visibility Graph Analysis of room to room typed museum. Visibility Graph Analysis derived detailed results in exhibit arrangement so it will be the useful method not only for architecture but also for planning of exhibit arrangement in open typed museum. Through this study, various possibilities on Quantitative Analysis Method of Museum Architecture could be verified. However, the analysis still has limitation of second dimension. Therefore, diverse and liberal following study will be expected to accomplish.