• 충청수학회지
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• 제19권1호
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• pp.37-47
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• 2006

In this paper we characterize the graphs whose inserted graphs are Hamiltonian, and we study the relationship between Hamiltonian graphs and inserted graphs. Also we prove that if a connected graph G contains at least 3 vertices then inserted graph of the square of G is Hamiltonian and if G contains at least 3 edges then the square of inserted graph of G is Hamiltonian.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 하계종합학술대회 논문집(3)
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• pp.63-66
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• 2002

In this paper, we consider the hamiltonian properties of m ${\times}$ n mesh networks with two wrap-around edges. We describe sufficient condition that at least two edges should be added to a mesh to make it hamiltonian-connected. We propose two graphs, M1(ｍ,n) and M2(ｍ,n). These are obtained by adding one and two edges respectively in the ｍ${\times}$ｎ mesh. We show the hamiltonian properties of M1(ｍ,n) and prove that M2(m, n) is hamiltonian-connected using the hamiltonian properties of M1(ｍ,n).

• 대한수학회지
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• 제45권6호
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• pp.1769-1784
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• 2008

The group Hameo (M, $\omega$) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, $\omega$) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the $L^{(1,{\infty})}$-Hofer norm (and not the $L^{\infty}$-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the $L^{\infty}$-case. In view of the fact that the Hofer norm on the group Ham (M, $\omega$) of Hamiltonian diffeomorphisms does not depend on the choice of the $L^{(1,{\infty})}$-norm vs. the $L^{\infty}$-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.

• 한국정보과학회논문지:시스템및이론
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• 제30권7_8호
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• pp.434-444
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• 2003

본 논문에서는 첫 행과 마지막 행에 두개의 랩어라운드 에지를 갖는 m$\times$n (m$\geq$2, n$\geq$3) 메쉬 연결망에서의 고장 해밀톤 성질들에 대해 고려한다. 제시한 연결망이 n이 홀수일 때 해밀톤 연결된 그래프이며 1-고장 해밀톤 사이클을 지님을 보인다. 그리고 n이 짝수일 때 강한 해밀톤 laceable 그래프이며 1-정점 고장 강한 해밀톤 laceable 그래프임을 보인다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.2079-2082
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• 2002

An interconnection network is called hamiltonian-connected if there exists a hamiltonian path joining every pair of nodes. We consider the problem of adding edges to a mesh to make it hamiltonian- connected. We show that at least two edges are necessary for the problem. Also, we present the method to add two edges to a mesh so that the resulting network is hamiltonian-connected.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.325-331
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• 2010

Let a and b be nonnegative integers with 2 $\leq$ a < b, and let G be a Hamiltonian graph of order n with n > $\frac{(a+b-5)(a+b-3)}{b-2}$. An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if $\delta(G)\;\geq\;\frac{(a-1)n+a+b-3)}{a+b-3}$ and $\delta(G)$ > $\frac{(a-2)n+2{\alpha}(G)-1)}{a+b-4}$.

• Bulletin of the Korean Chemical Society
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• 제6권5호
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• pp.309-311
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• 1985

When a molecule is perturbed by an external field, the perturbed moecue can be described as a doubly perturbed system. Hartree-Fock operator in the absence of the field is the zeroth order Hamiltonian, and a correlation operator and the external field operator are perturbations. The effective Hamiltonian, which is a projection of the total Hamiltonian onto a small finite subspace (usually a valence space), has been formally derived. The influence of the external field to the molecular Hamiltonian itself has been examined within an effective Hamiltonian framework. The first order effective expectation values, for instance electromagnetic transition amplitudes, between valence states are found to be easily calculated - by simply taking matrix elements of the effective external field operator. Implications of the terms in perturbation expansion are discussed.

• 대한수학회지
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• 제53권4호
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• 한국정보과학회논문지:시스템및이론
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• 제32권8호
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• pp.393-398
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• 2005

상호 연결망에서 해밀톤 경로는 선형 배열 구현이나 멀티캐스팅과 같은 여러 응용에서 활용된다. 본 논문에서는 여러 병렬 시스템의 상호연결망으로 사용되는 메쉬 연결망의 해밀톤 성질에 대해 고려한다. 연결망이 강한 해밀톤 laceable이면 그 연결망은 임의의 두 노드를 잇는 가능한 가장 긴 길이의 경로를 지닌다. 2차원 메쉬 M(m, n)은 노드의 수가 짝수이면 $m{\geq}4,\;n{\geq}4$일 때, 노드의 수가 홀수이면 $m{\geq}3,\;n{\geq}3$일 때 강한 해밀톤 laceable 그래프임을 보인다. 메쉬는 토러스, k-ary n-큐브, 하이퍼큐브, 재귀원형군과 같은 여러 상호 연결망들의 스패닝 부 그래프이므로 본 논문의 결과는 이들 연결망들의 고장 해밀톤 성질을 밝히는데 활용될 수 있다.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.507-519
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• 2009

We give a theorem of the existence of the multiple solutions of the Hamiltonian system with the square growth nonlinearity. We show the existence of m solutions of the Hamiltonian system when the square growth nonlinearity satisfies some given conditions. We use critical point theory induced from the invariant function and invariant linear subspace.