• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.83-93
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• 2006

A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper, by characterizing the circuit graphs and investigating the structure of LV-graphs, we extend his result to 3-connected infinite locally finite VAP-free plane graphs.

• 한국산업정보학회논문지
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• 제3권1호
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• pp.258-268
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• 1998

This paper presents two sequential advanced split and merge algorithms and a parallel image segmentation algorithm based on them. First, the two advanced methods are obtained from the combination of edge detection and classic split and merge to solve the inherent problems of the classical method. Besides, the parallel image segmentation algorithm on mesh-connected MIMD system considers three types in the merge stage to reduce the communication overhead between processors, such as intraprocessor merge, interprocessor with boundary merge, and interprocessor without boundary merge. Finally , we prove that the proposed algorithms achieve the improved performance by implementing them.

• Bulletin of the Korean Chemical Society
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• 제35권4호
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• pp.1177-1181
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• 2014

A 2D grid-like (4, 4)-connected topology coordination polymer, $[Co(BTA)_2(H_2O)_2]_n$ (1), where HBTA = 2-(1H-benzotriazol-1-yl)acetic acid, has been synthesized by hydrothermal method and characterized by single crystal X-ray diffraction, IR spectroscopy, elemental analysis and surface photovoltage spectroscopy (SPS). X-ray diffraction analyses indicated that 1 displays octahedral metal centers with secondary building units (SBUs) [$Co(BTA)_2(H_2O)_2$] bridged by the $BTA^-$ ligands. In the crystal, the 2D supramolecular architecture is further supported by $O-H{\cdots}O$, $O-H{\cdots}N$, $C-H{\cdots}O$ hydrogen bonds and ${\pi}{\cdots}{\pi}$ stacking interactions. The SPS of polymer 1 indicates that there are positive response bands in the range of 300-600 nm showing photo-electric conversion properties. There are good relationships between SPS and UV-Vis spectra.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.613-627
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• 2019

Consider a connected molecular graph G = (V, E) where V is the set of vertices and E is the set of edges. In G, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph G, every edge (say) e = uv will be connected by two atoms u and v. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n{\times}n}$.

• 대한수학회보
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• 제35권3호
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• pp.491-501
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• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.

• 대한수학회보
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• 제25권2호
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• pp.171-174
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• 1988

Let M be an n-dimensional compact connected and oriented Riemannian manifold isometrically immersed in an (n+2)-dimensional Euclidean space $R^{n+2}$. Moore [5] proved that if M is of positive curvature, then M is a homotopy sphere. This result is generalized by Baldin and Mercuri [2], Baik and Shin [1] to the case of non-negative curvature, which is stated as follows: If M of non-negative curvature, then M is either a homotopy sphere or diffeomorphic to a product of two spheres. In particular, if there is a point at which the curvature operator is positive, then M is homeomorphic to a sphere.e.

• 충청수학회지
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• 제22권2호
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• pp.211-216
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• 2009

Let G be a Denjoy domain and let G' a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G' into G. Let G and G' are N-connected. We know that if N = 2, there is a re-imbedding f of G' into G such that G - cl(f(G')) has an interior point. In this note, we obtain the following theorem. If $N{\geq}3$, G has a Denjoy proper subdomain G' such that, for any re-imbeddings f of G' into G, G - cl(f(G') has no interior point.

• 충청수학회지
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• 제22권2호
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• pp.229-234
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• 2009

Let f : $X{\rightarrow}X$ be a self-map of a connected finite polyhedron X. In this short note, we say that the mod H Nielsen number $N_H(f)$ is well-defined without the algebraic condition $ f_{\pi}(H)\;{\subseteq}H$ and that $N_H(f)$ is the same as the q-Nielsen number $N_q(f)$ in any case.

• 대한수학회지
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• 제54권5호
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• 대한수학회지
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• 제35권1호
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• pp.165-175
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• 1998

We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.