• 정보처리학회논문지A
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• 제13A권3호
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• pp.253-260
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• 2006

본 논문에서는 피라미드 그래프에서의 헤밀톤 사이클 특성을 분석한다. 사이클 확장 연산을 이용하여 사이클의 크기를 확대시켜 나가는 일련의 과정을 통하여 헤밀톤 사이클을 찾을 수 있는 제시된 알고리즘을 적용함으로써 임의의 높이 N인 피라미드 그래프 내에 길이 $(4^N-1)/3$인 헤밀톤 사이클이 존재함을 증명한다.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.221-225
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• 2016

For a connected graph G = (V, E), its inverse degree is defined as $\sum_{{\upsilon}{\in}{V}}^{}\frac{1}{d(\upsilon)}$. Using an upper bound for the inverse degree of a graph obtained by Cioabă in [4], we in this note present sufficient conditions for some Hamiltonian properties and k-connectivity of a graph.

• Journal of Information Processing Systems
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• 제7권1호
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• pp.75-84
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• 2011

The enhanced pyramid graph was recently proposed as an interconnection network model in parallel processing for maximizing regularity in pyramid networks. We prove that there are two edge-disjoint Hamiltonian cycles in the enhanced pyramid networks. This investigation demonstrates its superior property in edge fault tolerance. This result is optimal in the sense that the minimum degree of the graph is only four.

• 대한수학회논문집
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• 제11권4호
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• 산업경영시스템학회지
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• 제23권59호
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• pp.1-10
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• 2000

The traveling salesman problem is a representative NP-Complete problem. It needs lots of time to get a solution as the number of city increase. So, we need an efficient heuristic algorithm that gets good solution in a short time. Almost edges that participate in optimal path have somewhat low value cost. This paper discusses the property of nearest neighbor and 3-opt. This paper uses nearest neighbor's property to select candidate edge. Candidate edge is a set of edge that has high probability to improve cycle path. We insert edge that is one of candidate edge into intial cycle path. As two cities are connected. It does not satisfy hamiltonian cycle's rule that every city must be visited and departed only one time. This paper uses 3-opt's method to sustain hamiltonian cycle while inserting edge into cycle path. This paper presents a highly efficient heuristic algorithm verified by numerous experiments.

• Journal of Information Processing Systems
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• 제13권6호
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• pp.1554-1574
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• 2017

This paper introduces a new type of determining factor for Pseudo Random Strings (PRS). This classification depends upon a mathematical property called Finite Induction (FI). FI is similar to a Markov Model in that it presents a model of the sequence under consideration and determines the generating rules for this sequence. If these rules obey certain criteria, then we call the sequence generating these rules FI a PRS. We also consider the relationship of these kinds of PRS's to Good/deBruijn graphs and Linear Feedback Shift Registers (LFSR). We show that binary sequences from these special graphs have the FI property. We also show how such FI PRS's can be generated without consideration of the Hamiltonian cycles of the Good/deBruijn graphs. The FI PRS's also have maximum Shannon entropy, while sequences from LFSR's do not, nor are such sequences FI random.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2000년도 추계종합학술대회
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• pp.412-418
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• 2000

본 논문에서는 HCN(n,n)이 Hamiltonian Cycles을 갖는다는 것을 증명하고, HCN(n,n)과 HFN(n,n) 사이의 임베딩을 분석하고, HFN(n,n)과 2n-hypercube사이의 임베딩을 분석한다. HCN(n,n)을 HFN(n,n)에 연장율 3에 임베딩 가능함을 증명하고, HFN(n,n)을 HCN(n,n)에 임베딩하는 비용이 O(n)임을 증명하며, HFN(n,n)을 2n-hypercube애 연장율 3에 임베딩 가능함을 증명하고, 2n-hypercube을 HFN(n,n)에 임베딩하는 비용이 O(n)임을 증명한다

• Bulletin of the Korean Chemical Society
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• 제9권2호
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• pp.101-105
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• 1988

The ab initio effective valence shell Hamiltonian method, based on quasidegenerate many-body perturbation theory, is generalized to calculate molecular properties as well as the valence state energies which have previously been determined for atoms and small molecules. The procedure requires the evaluation of effective operator for each molecular property. Effective operators are perturbatively expanded in powers of correlation and contain contributions from excitations outside of the multireference valence space. To demonstrate the validity of this method, calculations for dipole moments of several low lying valence states of OH, $OH^+$, and $OH^-$ to first order in the correlations have been performed and compared with configuration interaction calculations.

• Bulletin of the Korean Chemical Society
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• 제19권9호
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• pp.985-993
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• 1998

The second order effective valence shell Hamiltonian ($H^v$), which is based on quasidegencrate many-body perturbation theory, is applied to determining the potential energy surfaces and the dipole moment functions of the various valence states of $NH_2$. The $H^v$ calculated values are found to be in good agreement with those of other ab initio calculations or experiments. It signifies the fact that the $H^v$ is a good ab initio method to describe the energies and properties of various valence states with a same chemical accuracy. Furthermore, it is shown that the lowest (second order for energy and the first order for property) order $H^v$ method is very accurate for small molecules like $NH_2$ and the matrix elements of Hv which are computed only once are all we need to accurately describe all the valence states simultaneously.

• 한국정보과학회논문지:시스템및이론
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• 제30권12호
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• pp.691-698
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• 2003

이 논문에서는 주어진 두 정점 사이에 다른 모든 정점을 정확히 한번 지나는 k개의 서로소인 경로가 존재하는가 하는 일대일 서로소인 경로 커버 문제를 제안한다. 임의의 k, 임의의 두 정점 사이에 일대일 서로소인 경로 커버를 가지는 그래프는 해밀톤 연결되어 있다는 것보다 강한 해밀톤 성질을 가진다. 재귀원형군에서 이 문제를 고찰하여, 임의의$k(1{\leq}k{\leq}m)$에 대해서 $ G(2^m,4)$, $m{\geq}3$은 임의의 두 정점 사이에 k개의 경로로 이루어진 일대일 서로소인 경로 커버가 존재함을 보인다.