• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.39-48
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• 2006

Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1159-1174
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• 1996

The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

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

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.75-86
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• 1996

Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1269-1287
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• 2006

As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.

• Journal of the Korean Mathematical Society
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• v.30 no.1
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• pp.229-249
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• 1993

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.114-117
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• 2009

A new video inpainting algorithm is proposed for removing unwanted objects or error of sources from video data. In the first step, the block bundle is defined by the motion information of the video data to keep the temporal consistency. Next, the block bundles are arranged in the 3-dimensional graph that is constructed by the spatial and temporal correlation. Finally, we pose the inpainting problem in the form of a discrete global optimization and minimize the objective function to find the best temporal bundles for the grid points. Extensive simulation results demonstrate that the proposed algorithm yields visually pleasing video inpainting results even in a dynamic scene.

• Journal of Advanced Information Technology and Convergence
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• v.9 no.1
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• pp.103-113
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• 2019

Motivation: Polymerized actin-based cytoskeletal structures are crucial in shape, dynamics, and resilience of a cell. For example, dynamical actin-containing ruffles are located at leading edges of cells and have a significant impact on cell motility. Other filamentous actin (F-actin) bundles, called stress fibers, are essential in cell attachment and detachment. For this reason, their mechanistic understanding provides crucial information to solve practical problems related to cell interactions with materials in tissue engineering. Detecting and counting actin-based structures in a cellular ensemble is a fundamental first step. In this research, we suggest a new method to characterize F-actin wrapping fibers from confocal fluorescence image stacks. As fluorescently labeled F-actin often envelope the fibers, we first propose to segment these fibers by diminishing an energy based on maximum flow and minimum cut algorithm. The actual actin is detected through the use of bilateral filtering followed by a thresholding step. Later, concave actin bundles are detected through a graph-based procedure that actually determines if the considered actin filament is enclosing the fiber.