• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1397-1404
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• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• Metals and materials international
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• v.24 no.6
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• pp.1432-1437
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• 2018

This work investigated edge-cracking behavior of equiatomic CoCrFeMnNi high-entropy alloy during hot rolling at rolling temperatures $500{\leq}T_R{\leq}1000^{\circ}C$. Edge cracks did not form in the material rolled at $500^{\circ}C$, but widened and deepened into the inside of plate as $T_R$ increased from $500^{\circ}C$. Edge cracks were most severe in the material rolled at $1000^{\circ}C$. Mn-Cr-O type non-metallic inclusion and oxidation were identified as major factors that caused edge cracking. The inclusions near edge region acted as preferential sites for crack formation. Connection between inclusion cracks and surface cracks induced edge cracking. Rolling at $T_R{\geq}600^{\circ}C$ generated distinct inclusion cracks whereas they were not serious at $T_R=500^{\circ}C$, so noticeable edge cracks formed at $T_R{\geq}600^{\circ}C$. At $T_R=1000^{\circ}C$, significant oxidation occurred at the crack surface. This accelerated edge crack penetration by embrittling the crack tip, so severe edge cracking occurred at $T_R=1000^{\circ}C$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.2006-2010
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• 2005

This study is concerned with the relation between steelbelt and belt edge separation. Belt edge separation causes tire burst and threatens passenger's safety. For that reason, it is important to predict durability caused by belt edge separation first in tire structure design step. In this study, to predict belt edge separation, we suggest the prediction method of belt edge separation and evaluate the effect of steelbelt width on the belt edge separation using FEM. We study on analysis parameter also to do exact estimation about the shear behaviour of belt edge area.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.23-30
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• 2014

For two positive integers r and s, $\mathcal{G}$(n; r; ${\theta}_s$) denotes to the class of graphs on n vertices containing no r of edge disjoint ${\theta}_s$-graphs and f(n; r; ${\theta}_s$) = max{${\varepsilon}(G)$ : G ${\in}$ $\mathcal{G}$(n; r; ${\theta}_s$)}. In this paper, for integers r, $k{\geq}2$, we determine f(n; r; ${\theta}_{2k+1}$) and characterize the edge maximal members in G(n; r; ${\theta}_{2k+1}$).

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.871-882
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• 2012

For a connected graph G of order $n$, an ordered set $S=\{u_1,u_2,{\cdots},u_k\}$ of vertices in G is a linear edge geodetic set of G if for each edge $e=xy$ in G, there exists an index $i$, $1{\leq}i$ < $k$ such that e lie on a $u_i-u_{i+1}$ geodesic in G, and a linear edge geodetic set of minimum cardinality is the linear edge geodetic number $leg(G)$ of G. A graph G is called a linear edge geodetic graph if it has a linear edge geodetic set. The linear edge geodetic numbers of certain standard graphs are obtained. Let $g_l(G)$ and $eg(G)$ denote the linear geodetic number and the edge geodetic number, respectively of a graph G. For positive integers $r$, $d$ and $k{\geq}2$ with $r$ < $d{\leq}2r$, there exists a connected linear edge geodetic graph with rad $G=r$, diam $G=d$, and $g_l(G)=leg(G)=k$. It is shown that for each pair $a$, $b$ of integers with $3{\leq}a{\leq}b$, there is a connected linear edge geodetic graph G with $eg(G)=a$ and $leg(G)=b$.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.671-677
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• 2021

For a distance-regular graph with valency k, second largest eigenvalue r and diameter D, it is known that r ≥ $min\{\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2},\;a_3\}$ if D = 3 and r ≥ $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ if D ≥ 4, where λ = a₁. This result can be generalized to the class of edge-regular graphs. For an edge-regular graph with parameters (v, k, λ) and diameter D ≥ 4, we compare $\frac{{\lambda}+\sqrt{{\lambda}^2+4k}}{2}$ with the local valency λ to find a relationship between the second largest eigenvalue and the local valency. For an edge-regular graph with diameter 3, we look at the number $\frac{{\lambda}-\bar{\mu}+\sqrt{({\lambda}-\bar{\mu})^2+4(k-\bar{\mu})}}{2}$, where $\bar{\mu}=\frac{k(k-1-{\lambda})}{v-k-1}$, and compare this number with the local valency λ to give a relationship between the second largest eigenvalue and the local valency. Also, we apply these relationships to distance-regular graphs.

• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.579-586
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• 2002

The edge descriptor proposed by MPEG-7 standard is a representative approach for the contents-based image retrieval using the edge information. In the edge descriptor, the edge information is the edge histogram derived from a gray-level value image. This paper proposes a new method which extracts color edge information from color images and a new approach for the contents-based image retrieval based on the color edge histogram. The poposed method and technique are applied to image retrieval of the e-catalogue. For the evaluation, the results of image retrieval using the proposed approach are compared with those of image retrieval using the edge descriptor by MPEG-7 and the statistics shows the efficiency of the proposed method. The proposed color edge model is made by combining the R,G,B channel components vectorially and by characterizing the vector norm of the edge map. The color edge histogram using the direction of the color edge model is subsequently used for the contents-based image retrieval.

• Journal of Biosystems Engineering
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• v.4 no.1
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• pp.1-23
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• 1979

The use of barley seeder attached to rotary tiller in the rural area has a significant meaning not only for the solution of labor peak season, but also for the increase of land utilization efficiency. The facts that presently being used barley seeders are all based on the mechanical principles of the reverse rotation, center drive and are all using forward rotating tine, which is used to be easily and heavily worn out when it rotates reversely, raise problem of recommending them to rural area in Korea. Therefore, the main objective of the study was to develop new type of rotary tine attachable to barley seeders. To attain the objective the following approaches were applied. (1) The kinematic analysis of reverse rotating barley seeders. (2) The studies on the soil bin and artificial soil. (3) The comparative experiment on the power requirement of prototype tine. The results obtained from the studies are summarized as follow: 1. The kinematic analysis of barley seeder attached to rotary tiller: The following results were obtained from the kinematic analysis for deriving general formulae of the motion and velocity characterizing the rotary tine of barley seeders presently being used by farmers. a) The position vector (P) of edge point (P) in the rotary tine of reverse rotating, center drive was obtained by the following formula. $$P=(vt+Rcos wt)i+Rsin wt j+ \{ Rcos \theta r sin \alpha cos (wt- \beta +\theta r) +Rsin \theta r sin \alpha sin (wt-\beta + \theta r) \} lk $$ b) The velocity of edge point $(P^')$ of reverse rotating, center drive rotary tine was obtained by the following formula. $$(P^')=(V-wR sin wt)i+(w\cdot Rcoswt)j + \{ -w\cdot Rcos \theta r\cdot sin \alpha \cdot sin (wt-\beta +\theta r) + w\cdot Rsin \theta r\cdot sin \alpha \cdot cos (wt- \beta + \theta r \} k $$ c) In order to reduce the power requirement of rotary tine, the angle between holder and edge point was desired to be reduced. d) In order to reduce the power requirement, the edge point of rotary tine should be moved from the angle at the begining of cutting to center line of machine, and the additional cutting width should be also reduced. 2. The studies on the soil bin and artificial soil: In order to measure the power requirement of various cutting tines under the same physical condition of soil, the indoor experiments Viere conducted by filling soil bin with artificially made soil similar to the common paddy soil and the results were as follows: a) When the rolling frequencies$(x)$ of the artificial soil were increased, the densIty$(Y)$ was also increased as follows: $$y=1.073200 +0.070780x - 0.002263x^2 (g/cm^3)$$ b) The absolute hardness $(Y)$ of soil had following relationship with the rolling frequencies$(x)$ and were increased as the rolling frequencies were increased. $$Y=37.74 - \frac {0.64 + 0.17x-0. 0054x^2} {(3.36-0.17x + 0.0054x^2)^3} (kg/cm^3)$$ c) The density of soil had significant effect on the cohesion and angle of internal friction of soil. For instance, the soil with density of 1.6 to 1.75 had equivalent density of sandy loam soil with 29.5% of natural soil moisture content. d) The coefficient of kinetiic friction of iron plate on artificial soil was 0.31 to 0.41 and was comparable with that of the natural soil. e) When the pulling speed of soil bin was the 2nd forward speed of power tiller, the rpm of driving shaft of rotary was similar to that of power tiller, soil bin apparatus is indicating the good indoor tester. 3. The comparative experiment on the power requirement of prototype tine of reverse rotating rotary: According to the preliminary test of rotary tine developed with various degrees of angle between holder and edge pcint due to the kinematic analysis, comparative test between prototype rotary tine with $30 ^\circ $ and $10 ^\circ$ of it and presently being used rotary tine was carried out 2nd the results were as follows: a) The total cutting torque was low when the angle between holder and edge point was reduced. b) $\theta r$ (angle between holder and edge point) of rotary tine seemed to be one: of the factors maximizing the increase of torque. c) As the angle between holder and edge point ($\theta r$) of rotary tine was $30 ^\circ $ rather than $45 ^\circ $, the angle of rotation during cutting soil was reduced and the total cutting torque was accordingly reduced about 10%, and the reduction efficiency of total cutting torque was low when the angle between holder and edge point ($\theta r$) of rotary tine was $10 ^\circ $, which indicates that the proper angle between holder and edge point of rotary tine should be larger than $10 ^\circ $ and smaller than $30 ^\circ $ . From above results, it could be concluded that the use of the prototype rotary tine which reduced the angle between holder and edge point to $30 ^\circ $, insted of $45 ^\circ $, is disirable not only decreasing the power requirements, but also increasing the durabie hour of it. Also forward researches are needed, WIlich determine the optimum tilted angle of rotary brocket, and rearrangement of the rotary tine on the rotary boss.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.669-682
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• 2016

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.