• Journal of KIISE:Computer Systems and Theory
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• v.29 no.12
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• pp.665-679
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• 2002

The fault diameter of a graph G is the maximum of lengths of the shortest paths between all two vertices when there are $\chi$(G) - 1 or less faulty vertices, where $\chi$(G) is connectivity of G. In this paper, we analyze the fault diameter of recursive circulant $G(2^m,2^k)$ with $k{\geq}3$. Let $ dia_{m.k}$ denote the diameter of $G(2^m,2^k)$. We show that if $2{\leq}m,2{\leq}k, the fault diameter of $G(2{\leq}m,2{\leq}k)$ is equal to $2^m-2$, and if m=k+1, it is equal to $2^k-1$. It is also shown that for m>k+1, the fault diameter is equal to di a_$m{\neq}1$(mod 2k); otherwise, it is less than or equal to$dia_{m.k+2}$.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.589-591
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• 2001

본 논문에서는 재귀원형군 G(2$^{m}$ , 2$^{k}$ )에서 노드에 고장이 났을 경우 임의의 두 노드사이의 고장이 없는 최단경로의 길이를 분석한다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 m = nk+r이라 하자. 여기서 n $\geq$ 이고, 1$\leq$ r$\leq$ k이다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 임의의 연결도-1개 이하의 노드에 고장이 있을 경우, 모든 두 노드 사이의 고장이 없는 가장 짧은 경로들의 길이의 최대값, 즉 G(2$^{m}$ , 2$^{k}$ )의 고장지름은 n이 짝수이면 di $a_{m, k}$+2 이하이고, n이 흘수이면 di $a_{m, k}$+3 이하이다. 여기서 di $a_{m, k}$는 G(2$^{m}$ , 2$^{k}$ )의 지름이다.

• Journal of Animal Environmental Science
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• v.12 no.3
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• pp.115-122
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• 2006

This study investigated the spatial distribution of dust originating from tunnel-ventilated windowless broiler building measuring 12 m wide, 61 m long, with a side wall height of 3 m and a capacity of 16,982 birds. Dust concentrations in terms of total suspended particles (TSP), and particulate matter of sizes $10\;{\mu}m$(PM10), $2.5\;{\mu}m$(PM2.5), and $1\;{\mu}m(PM1)$ were measured at 30 minutes interval by using GRIMM Aerosol Monitor (GRIMM AEROSOL). The spatial distribution of dust showed the lower dust concentration in the inlet than in the outlet of the tunnel ventilation, and dust concentration decreasing as the dust size decreased, as follows: $317.9\;{\mu}g/m^3$ TSP; $74.7{\mu}m/m^3$ PM10; $9.7\;{\mu}g/m^3$ PM2.5; and $6.2\;{\mu}g/m^3$ PM1 in the inlet; and $2,678.5\;{\mu}g/m^3$ TSP; $555.5\;{\mu}g/m^3$ PM10; $33.3\;{\mu}g/m^3$ PM2.5; and $10.2\;{\mu}g/m^3$ PM1 in the outlet. The dust concentration emitted from the tunnel ventilated fan was $446.6\;{\mu}g/m^3$ TSP; $129.1\;{\mu}g/m^3$ PM10; $15.8\;{\mu}g/m^3$ PM2.5; and $6.1\;{\mu}g/m^3$ PM1 in the 3 meters from the fan and $25.1\;{\mu}g/m^3$ TSP; $8.8\;{\mu}g/m^3$ PM10; $5.6\;{\mu}g/m^3$ PM2.5; and $4.9\;{\mu}g/m^3$ PM1 in the 50 meters from the fan.

• Korean Journal of Veterinary Research
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• v.30 no.4
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• pp.407-412
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• 1990

This study was designed to elucidate the effects of administration with dietary iron and fat-free diet on the contents of unsaturated fatty acid in phospholipid molecules, vitamin E contents and malondialdehyde contents in liver, kidney, muscle and testis of the male rats. The rats were divided into 3 experimental groups, namely, control, iron injection and fat-free diet administration groups. The control group was fed with normal diet, iron injection group injected intraperitoneally 20mg of ferric hydroxide/100g of body weight 20 times every 3 days and fat-free diet group administered lipid extraction diet with hexane in normal diet. All experimental groups were maintained for 60 days with feeding on the respective ration. The results obtained were summarized as follows: 1. In the mean contents of unsaturated fatty acid in phospholipid of liver, kidney, muscle and testis among groups, control group was 21.31mg/g, 19.38mg/g, 1.67mg/g, 13.68mg/g, iron injection group was 13.83mg/g, 16.53mg/g, 0.71mg/g, 10.11mg/g and fat-free diet group was 21.07mg/g, 19.38mg/g, 1.49mg/g and 13.40mg/g, respectively. 2. In the mean contents of vitamin E in liver, kidney, muscle and testis among groups, control group was 6.77mg/g, 1.93mg/g, 0.12mg/g, 0.17mg/g, iron injection group was 3.16mg/g, 0.86mg/g, 0.07mg/g, 0.09mg/g and fat-free diet group was 7.41mg/g, 1.50mg/g, 0.11mg/g and 0.16mg/g, respectively. 3. In the mean contents of malondialdehyde in liver, kidney, muscle, testis and serum among groups, control group was 11.29nM/0.1g, 23.25nM/0.1g, 42.47nM/0.1g, 7.01nM/0.1g, 4.33nM/ml, iron injection group was 34.98nM/0.1g, 40.55nM/0.1g, 72.21nM/0.1g, 12.26nM/0.1g, 11.27nM/ml and fat-free diet group was 8.07nM/0.1g, 20.63nM/0.1g, 39.92nM/0.1g, 6.95nM/0.1g and 4.27nM/ml, respectively.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.8
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• pp.426-431
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• 2005

A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate many-to-many 2-DPC in a double loop network G(mn;1,m), and show that every nonbipartite G(mn;1,m), $m{\geq}3$, has 2-DPC joining any two source-sink pairs of vertices and that every bipartite G(mn;1,m) has 2-DPC joining any two source-sink pairs of black-white vertices and joining any Pairs of black-black and white-white vertices. G(mn;l,m) is bipartite if and only if n is odd and n is even.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.1009-1023
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k ) 그래프 이론적 관점에서 고찰하고 정점이 서로소인 경로에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )의 서로 다른 두 노드 v와 w를 잇는 연결도 kappa(G)개의 서로소인 경로의 길이가 두 노드 사이의 거리d(v,w)나 혹은 G(2^m , 2^k )의 지름 \dia(G)에 비해서 얼마나 늘어나는지를 고려한다. 서로소인 경로를 재귀적으로 설계하는데, 그 길이는 k ge2일 때 d(v,w)+2^k-1과 \dia(G)+2^k-1의 최솟값 이하이고, k=1일 때 d(v,w)+3과 \dia(G)\+2의 최솟값 이하이다. 이 연구는 (2^m , 2^k )의 고장 감내 라우팅, 고장 지름이나 persistence의 분석에 이용할 수 있다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties concerned with node-disjoint paths. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . We consider the length increments of {{{{kappa(G)disjoint paths joining arbitrary two nodes v and win G(2^m , 2^k )compared with distance d(v,w)between the two nodes and diameter {{{{\dia(G)of G(2^m , 2^k ), where kappa(G)is the connectivity of G(2^m , 2^k ). We recursively construct disjoint paths of length less than or equal to the minimum of {{{{d(v,w)+2^k-1and \dia(G)+2^k-1for kge2 and the minimum of d(v,w)+3 and \dia(G)+2for k=1. This work can be applied to fault-tolerant routing and analysis of fault diameter and persistence of G(2^m , 2^k )

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.793-807
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• 2012

If G is any connected graph of order p; then the thorn graph $G_p^*$ with code ($n_1$, $n_2$, ${\cdots}$, $n_p$) is obtained by adding $n_i$ pendent vertices to each $i^{th}$ vertex of G. By treating the pendent edge of a thorn graph as $P_2$, $K_2$, $K_{1,1}$, $K_1{\circ}K_1$ or $P_1{\circ}K_1$, we generalize a thorn graph by replacing $P_2$ by $P_m$, $K_2$ by $K_m$, $K_{1,1}$ by $K_{m,n}$, $K_1{\circ}K_1$ by $K_m{\circ}K_1$ and $P_1{\circ}K_1$ by $P_m{\circ}K_1$ and their respective generalized thorn graphs are denoted by $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ respectively. Many chemical compounds can be treated as $G_P$, $G_K$, $G_B$, $G_{KK}$ and $G_{PK}$ of some graphs in graph theory. In this paper, we obtain the bounds of the wiener index for these generalization of thorn graphs.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.261-271
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• 2007

The symbol C($m_1^{n_1}m_2^{n_2}{\cdots}m_s^{n_s}$) denotes a 2-regular graph consisting of $n_i$ cycles of length $m_i,\;i=1,\;2,\;{\cdots},\;s$. In this paper, we give some construction methods of cyclic($K_v$, G)-designs, and prove that there exists a cyclic($K_v$, G)-design when $G=C((4m_1)^{n_1}(4m_2)^{n_2}{\cdots}(4m_s)^{n_s}\;and\;v{\equiv}1(mod\;2|G|)$.

• The Korean Journal of Ecology
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• v.28 no.6
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• pp.347-351
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• 2005

The amounts of organic carbon and several nutrients in litterfall on the forest floor of Quercus mongolica forest were assessed for two years from 1998 through 2000 in Mt. Songnisan National Park in Korea. The amounts of organic carbon (C) in litterfall were the highest in autumn with the values of $150.4g/m^2$ (62.6%) in 1998 and $219.2g/m^2$ (61.0%) in 1999. In winter, organic C was the lowest with the values of $16.3g/m^2$ (6.8%) in 1998 and $12.5g/m^2$ (6.7%) in 1999. It was estimated that the organic C added to forest floor via litterfall was 240.1 $g{\cdot}m^{-2}yr^{-1}$ and 186.6 $g{\cdot}m^{-2}yr^{-1}$ 1998 and 1999, respectively. The amounts of nitrogen (N) in litterfall were the highest in autumn with the values of 5.9 $g/m^2$ (58.0%) in 1998 and 5.2 $g/m^2$ (62.3%) in 1999. The amount of phosphorus (P) in litterfall showed its peak in autumn with 0.19 $g/m^2$ (52.9%) in 1998 and 0.11 $g/m^2$ (52.6%) in 1999. The amount of P returned to forest floor via litterfall was 0.35 $g{\cdot}m^{-2}yr^{-1}$ in 1998 and 0.22 $g{\cdot}m^{-2}yr^{-1}$ in 1999. The amount of potassium (K) in litterfall showed its peak in autumn with 0.57 $g/m^{2}$ (53.8%) in 1998 and 0.42 $g/m^2$ (55.3%) in 1999. The amounts of K returned to forest floor via litterfall was 1.11 $g{\cdot}m^{-2}yr^{-1}$ in 1998 and 0.81 $g{\cdot}m^{-2}yr^{-1}$ in 1999.