• The KIPS Transactions:PartA
• /
• v.11A no.5
• /
• pp.341-346
• /
• 2004

Recently A Hyper-Star Graph HS(m, k) has been introduced as a new interconnection network of new topology for parallel processing. Hyper-Star Graph has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show that Hyper-Star Graph HS(m, k) is subgraph of hypercube. And we also show that regular graph, Hyper-Star Graph HS(2n, n) is node-symmetric by introduced mapping algorithm. In addition, we introduce an efficient one-to-all broadcasting scheme - takes 2n-1 times - in Hyper-Star Graph HS(2n, n) based on a spanning tree with minimum height.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.1-30
• /
• 2020

In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots admit Dehn surgery yielding either Seifert-fibered spaces or graph manifolds at a surface slope. We show that middle/hyper doubly Seifert twisted torus knots admit the latter, that is, non-Seifert-fibered graph manifolds whose decomposing pieces consist of two Seifert-fibered spaces over the disk with two exceptional fibers.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.65-75
• /
• 2007

A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted ${\chi}$(H)) equals the number of vertices in the largest clique in H (denoted ${\omega}$(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n<13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.

• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.663-680
• /
• 2024

The zero divisor graph is the most basic way of representing an algebraic structure as a graph. For any commutative ring R, each element is a vertex on the zero divisor graph and two vertices are defined as adjacent if and only if the product of those vertices equals zero. In this research, we determine some topological indices such as the Wiener index, the edge-Wiener index, the hyper-Wiener index, the Harary index, the first Zagreb index, the second Zagreb index, and the Gutman index of zero divisor graph of integers modulo prime power and its direct product.

• The Pure and Applied Mathematics
• /
• v.26 no.3
• /
• pp.177-188
• /
• 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 applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.319-330
• /
• 2016

The hyper-Zagreb index HM(G) of a simple graph G is defined as the sum of the terms (d_u+d_v)² over all edges uv of G, where d_u denotes the degree of the vertex u of G. In this paper, we present several upper and lower bounds on the hyper-Zagreb index in terms of some molecular structural parameters and relate this index to various well-known molecular descriptors.

• The Journal of the Convergence on Culture Technology
• /
• v.9 no.1
• /
• pp.649-654
• /
• 2023

This paper proposes the design of a neural network structure search model using graph convolutional neural networks. Deep learning has a problem of not being able to verify whether the designed model has a structure with optimized performance due to the nature of learning as a black box. The neural network structure search model is composed of a recurrent neural network that creates a model and a convolutional neural network that is the generated network. Conventional neural network structure search models use recurrent neural networks, but in this paper, we propose GC-NAS, which uses graph convolutional neural networks instead of recurrent neural networks to create convolutional neural network models. The proposed GC-NAS uses the Layer Extraction Block to explore depth, and the Hyper Parameter Prediction Block to explore spatial and temporal information (hyper parameters) based on depth information in parallel. Therefore, since the depth information is reflected, the search area is wider, and the purpose of the search area of the model is clear by conducting a parallel search with depth information, so it is judged to be superior in theoretical structure compared to GC-NAS. GC-NAS is expected to solve the problem of the high-dimensional time axis and the range of spatial search of recurrent neural networks in the existing neural network structure search model through the graph convolutional neural network block and graph generation algorithm. In addition, we hope that the GC-NAS proposed in this paper will serve as an opportunity for active research on the application of graph convolutional neural networks to neural network structure search.

• The Transactions of the Korea Information Processing Society
• /
• v.6 no.7
• /
• pp.1756-1769
• /
• 1999

Parallel paths in an interconnection network have some significance in that message transmission time can be reduced because message is divided into packets and transmitted in parallel through several paths, and also an whose nodes has 2n binary bit string, is an interconnection network which has a lower network cost than hypercube and its variation. In this paper, we analyze node disjoint parallel path in Folded Hyper-Star graph FHS(2n,n) proposed as the topology of parallel computers and, using the result, prove that the fault diameter of a Folded Hyper-Star graph FHS(2n,n) is 2n-1.

• Journal of KIISE:Software and Applications
• /
• v.36 no.11
• /
• pp.936-946
• /
• 2009

A graph cuts method has recently attracted a lot of attentions for image segmentation, as it can globally minimize energy functions composed of data term that reflects how each pixel fits into prior information for each class and smoothness term that penalizes discontinuities between neighboring pixels. In previous approaches to graph cuts-based automatic image segmentation, GMM(Gaussian mixture models) is generally used, and means and covariance matrixes calculated by EM algorithm were used as prior information for each cluster. However, it is practicable only for clusters with a hyper-spherical or hyper-ellipsoidal shape, as the cluster was represented based on the covariance matrix centered on the mean. For arbitrary-shaped clusters, this paper proposes graph cuts-based image segmentation using mean shift analysis. As a prior information to estimate the data term, we use the set of mean trajectories toward each mode from initial means randomly selected in $L^*u^*{\upsilon}^*$ color space. Since the mean shift procedure requires many computational times, we transform features in continuous feature space into 3D discrete grid, and use 3D kernel based on the first moment in the grid, which are needed to move the means to modes. In the experiments, we investigate the problems of mean shift-based and normalized cuts-based image segmentation methods that are recently popular methods, and the proposed method showed better performance than previous two methods and graph cuts-based automatic image segmentation using GMM on Berkeley segmentation dataset.

• The KIPS Transactions:PartA
• /
• v.15A no.6
• /
• pp.345-350
• /
• 2008

Recently, a HyperStar network HS(2n,n) has been introduced as a new interconnection network of new topology for parallel processing. HyperStar network has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show a construction algorithm of edge-disjoint spanning trees in HyperStar network HS(2n,n). Also, we prove that edge-disjoint spanning tree by the algorithm is optimal.