• The KIPS Transactions:PartA
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• v.13A no.3 s.100
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• pp.253-260
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• 2006

In this paper, we analyze the Hamiltonian property of Pyramid graphs. We prove that it is always possible to construct a Hamiltonian cycle of length $(4^N-1)/3$ by applying the proposed algorithm to construct series of cycle expansion operations into two adjacent cycles in the Pyramid graph of height N.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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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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• v.7 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.59
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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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• v.13 no.6
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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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.10a
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• pp.412-418
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• 2000

In this paper, we will propose that HCN(n,n) gets Hamiltonian Cycles and analyze embedding among HCN(n,n) and UFN(n,n), and HFN(n,n) and In-hypercube. Further, we will prove that HCN(n,n) can be embedded into HFN(n,n) with dilation 3 and the cost for HFN(n,n) to be embedded into HCN(n,n) will be O(n), and HW(n,n) can be embedded into 2n-hypercube with dilation 3 and the cost for In-hypercube to be embedded into HFN(n,n) will be O(n).

• Bulletin of the Korean Chemical Society
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• v.9 no.2
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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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• v.19 no.9
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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.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.12
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• pp.691-698
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• 2003

In this paper, we propose a problem, called one-to-one disjoint path cover problem, whether or not there exist k disjoint paths joining a pair of vertices which pass through all the vertices other than the two exactly once. A graph which for an arbitrary k, has a one-to-one disjoint path cover between an arbitrary pair of vertices has a hamiltonian property stronger than hamiltonian-connectedness. We investigate this problem on recursive circulants and prove that for an arbitrary k $k(1{\leq}k{\leq}m)$$ G(2^m,4)$,$m{\geq}3$, has a one-to-one disjoint path cover consisting of k paths between an arbitrary pair of vortices.