• 정보처리학회논문지A
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• 제18A권6호
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• pp.225-232
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• 2011

Restricted Hypercube-Like(RHL) 그래프는 교차큐브, 뫼비우스큐브, 엠큐브, 꼬인큐브, 지역꼬인큐브, 다중꼬인큐브, 일반꼬인큐브와 같이 유용한 상호연결망들을 광범위하게 포함하는 그래프군이다. 본 논문에서는 $m{\geq}4$ 인 m-차원 RHL 그래프 G에 대해서 임의의 에지 집합 $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, 가 고장일 때, 고장 에지들을 제거한 그래프 $G{\setminus}F$는 임의의 서로 다른 두 정점 s와 t에 대해서 dist(s, V(F))${\neq}1$ 이거나 dist(t, V(F))${\neq}1$이면 해밀톤 경로가 있음을 보인다. V(F)는 F에 속하는 에지들의 양 끝점들의 집합이고 dist(v, V(F))는 정점 v와 집합 V(F)의 정점들 간의 최소 거리이다.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 대한수학회지
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• 제45권6호
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.27-40
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• 2002

For two integers m, n with m $\leq$ n, an [m,n]-factor F in a graph G is a spanning subgraph of G with m $\leq$ d$\_$F/(v) $\leq$ n for all v ∈ V(F). In 1996, H. Enomoto et al. proved that every 3-connected Planar graph G with d$\_$G/(v) $\geq$ 4 for all v ∈ V(G) contains a [2,3]-factor. In this paper. we extend their result to all 3-connected locally finite infinite planar graphs containing no unbounded faces.

• 한국정보처리학회논문지
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• 제6권8호
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• pp.2124-2132
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• 1999

Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

• 한국표면공학회지
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• 제55권4호
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• pp.196-201
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• 2022

This paper deals with anodic oxidation behavior of AZ31 Mg alloy in aqueous solutions containing various NaF concentrations from 0.01 M to 1 M. Three different voltage-time curves and anodic oxide formation behaviors appeared with concentration of NaF in deionized water. When NaF concentration is lower than 0.02 M, the voltage of AZ31 Mg alloy increased linearly and then reached a steady-state value more than 200 V, and large size pits and thin oxide layer were formed. When NaF concentration is between 0.05 M and 0.1 M, the voltage of AZ31 Mg alloy showed large periodic fluctuations of about 30 ~ 50 V around more than 200 V and large number of small particles were observed. If NaF concentration is higher than 0.2 M, PEO films can be formed without visible arcs under solution pH 6.5 ~ 7.5 by F^- ions without help of OH^- ions.

• 천문학논총
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• 제30권2호
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• pp.183-187
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• 2015

We use ALLWISE data release W1- and W2-band epoch photometry collected by the Wide-Field Infrared Survey Explorer (WISE) to determine slopes of the period-luminosity relations for RR Lyrae stars in 15 globular clusters in the corresponding bands. We further combine these results with V- and K-band photometry of Galactic field RR Lyrae stars to determine the metallicity slopes of the log $P_F-[Fe/H]-M_K$, log $P_F-[Fe/H]-M_{W1}$, and log $P_F-[Fe/H]-M_{W2}$ period-metallicity-luminosity relations. We infer the zero points of these relations and determine the kinematical parameters of thick-disk and halo RR Lyraes via statistical parallax, and estimate the RR Lyrae-based distances to 18 Local-Group galaxies including the center of the Milky Way.

• 한국정보과학회논문지:시스템및이론
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• 제31권1_2호
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• pp.86-94
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• 2004

이 논문에서는 재귀원형군 $ G(2^m, 4), m{\geq}3$은 고장인 요소의 수가 m-2개 이하일 때, 임의의 1, 4 ${\leq}1{\leq}2^m-f_v$에 대하여 길이 1인 고장 없는 사이클을 가짐을 보인다. 여기서, f$_{v}$ 는 고장 정점의 수이다. 이를 위하여, ｜F｜$\leq$k인 임의의 고장 요소 집합 F에 대해서 G-F가 임의의 두 정점을 잇는 길이가 해밀톤 경로보다 하나 작은 경로를 가질 때, G를 k-고장 하이포해밀톤 연결된 그래프라고 정의하고, $ G(2^m, 4), m{\geq}3$은 m-3-고장 하이포해밀톤 연결된 그래프임을 보인다.

• 대한수학회보
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• 제55권3호
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• pp.921-935
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• 2018

In this study we determine the structure of m-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of m-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.

• The Korean Journal of Physiology
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• 제17권1호
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• pp.1-11
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• 1983

1) 토끼동방결절의 작은 절편에 미세 전극 두개로 voltage clamp를 하고 과분극에 의하여 활성화되는 내향전류, $i_f$의 동력학적 성상을 분석하였다. 2) 전류 $i_f$는 $10^{-7}g/ml$ TTX와 2 mM $Mn^{2+}$의 존재하에서 과분극 pulse에 의하여 활성화되었으며 그 범위는 $-45\;mV{\sim}-75\;mV$였다. 전류의 크기와 시간경과는 막전압이 과분극될수록 커지고 빨라졌다. 3) Envelope test결과 $i_f$전류는 단일 gate에 의하여 지수합수적 (exponential)으로 조절됨을 보였다. 4) 2 mM의 $Ba^{2+}$에 의하여$i_f$전류의 크기는 감소하고 시간경과도 느려졌으며 반응속도상수와 gating molecule의 열리고 닫히는 반응계수(rate coefficient; ${\alpha}_s$, ${\beta}_s$)와 막전압 관계곡선을 과분극쪽으로 이동시켰다. 이러한 $Ba^{2+}$의 효과는 24 mM $K^+$에 의하여 일부 상쇄되었다.