• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.383-388
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• 2007

A (g, f)-factor F of a graph G is Called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. The binding number of G is defined by $bind(G)\;=\;{min}\;\{\;{\frac{{\mid}N_GX{\mid}}{{\mid}X{\mid}}}\;{\mid}\;{\emptyset}\;{\neq}\;X\;{\subset}\;V(G)},\;{N_G(X)\;{\neq}\;V(G)}\;\}$. Let G be a connected graph, and let a and b be integers such that $4\;{\leq}\;a\;<\;b$. Let g, f be positive integer-valued functions defined on V(G) such that $a\;{\leq}\;g(x)\;<\;f(x)\;{\leq}\;b$ for every $x\;{\in}\;V(G)$. In this paper, it is proved that if $bind(G)\;{\geq}\;{\frac{(a+b-5)(n-1)}{(a-2)n-3(a+b-5)},}\;{\nu}(G)\;{\geq}\;{\frac{(a+b-5)^2}{a-2}}$ and for any nonempty independent subset X of V(G), ${\mid}\;N_{G}(X)\;{\mid}\;{\geq}\;{\frac{(b-3)n+(2a+2b-9){\mid}X{\mid}}{a+b-5}}$, then G has a Hamiltonian (g, f)-factor.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.311-322
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• 2006

For the Briot-Bouquet differential equations of the form given in [1] $${{\mu}(z)+\frac {z{\mu}'(z)}{z\frac {f'(z)}{f(z)}\[\alpha{\mu}(z)+\beta]}=g(z)$$ we can reduce them to $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$ where $$v(z)=\alpha{\mu}(z)+\beta,\;h(z)={\alpha}g(z)+\beta\;and\;F(z)=f(z)/f'(z)$$. In this paper we are going to give conditions in order that if u and v satisfy, respectively, the equations (1) $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$, $${{\mu}(z)+G(z)\frac {v'(z)}{v(z)}=g(z)$$ with certain conditions on the functions F and G applying the concept of strong subordination $g\;\prec\;\prec\;h$ given in [2] by the author, implies that $v\;\prec\;{\mu},\;where\;\prec$ indicates subordination.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.357-366
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• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.573-581
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• 2018

In this paper we consider all orientation-preserving ${\mathbb{Z}}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (${\Gamma}(v)$, G(v)) in canonical form for some 5-tuple v = (r, s, t, m, n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (${\Gamma}(v)$, G(v)) that are homeomorphic to the quotient spaces $V_g/{\mathbb{Z}}_{p^2}$ of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_{p^2}$-actions on such handlebodies, up to equivalence.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.127-133
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• 2005

An f-coloring of a graph G = (V, E) is a coloring of edge set E such that each color appears at each vertex v $\in$ V at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index $\chi'_f(G)$ of G. Any graph G has f-chromatic index equal to ${\Delta}_f(G)\;or\;{\Delta}_f(G)+1,\;where\;{\Delta}_f(G)\;=\;max\{{\lceil}\frac{d(v)}{f(v)}{\rceil}\}$. If $\chi'_f(G)$= ${\Delta}$f(G), then G is of $C_f$ 1 ; otherwise G is of $C_f$ 2. In this paper, the classification problem of complete graphs on f-coloring is solved completely.

• Proceedings of the KIEE Conference
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• 2015.07a
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• pp.469-470
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• 2015

V2G를 활성화기 위해서는 전기차 보급이 우선이며, 보급에 따라 충전인프라 구축도 이루어져야 할 것이다. 해외에서는 전기차 보급과 충전인프라 구축을 위해 많은 보조금 지급, 세금 감면, 의무화 제도, 기타 혜택 등을 통해 V2G를 활성화 하기 위한 기본적인 사항들을 준비 중에 있으며, 실제로 많은 성장을 통해 보급도 상당하게 되었음을 알 수 있었다. 위에 언급하였던 전기자와 충전인프라가 기본적으로 구축이 되었다면 그 뒤에 설계를 해야 할 부문은 충 방전 요금제로 보인다. V2G를 통해 우리는 전력수요피크 삭감, 주파수예비조정, 비상발전 등의 용도로 사용을 할 수 있으며, 사용 목적에 따라 요금을 어떤 방식으로 적용이 될 것인지는 앞으로 연구가 필요하다고 판단된다. 현재 국내에는 전기차 충전요금제는 지정되어 사용되고 있는 실정이며, 방전요금제는 설계가 되어 있지 않다. 본 논문에서는 국내외 전기차 충전요금 사례를 비교하고 앞으로 V2G가 활성화 되었을 시 필요한 방전요금제 설계방향을 제시하고자 한다.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.3
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• pp.427-432
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• 2023

In this study, MEC (: Multi-access Edge Computing) proposes a cloud service network configuration for various tests of autonomous vehicles to which V2X (: Vehicle to Everything) is applied in Wave, LTE, and 5G networks and MEC App (: Application) applied V2X service function test verification of two domains (operator (KT, SKT, LG U+), network type (Wave, LTE (including 3G), 5G)) in a specific region. In 4G networks of domestic operators (SKT, KT, LG U+ and Wave), MEC summarized the improvement effects through V2X function blocks and traffic offloading for the purpose of bringing independent network functions. And with a high level of QoS value in the V2X VNF of the 5G network, the traffic steering function scenario was demonstrated on the destination-specific traffic path.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.59-74
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• 2017

A radio labeling of a graph G is a function $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ with the property that ${\mid}f(u)-f(v){\mid}{\geq}1+diam(G)-d(u,v)$ for every pair of vertices $u,v{\in}V(G)$, where diam(G) and d(u, v) are diameter and distance between u and v in the graph G respectively. The radio number of a graph G, denoted by rn(G), is the smallest integer k such that G admits a radio labeling. In this paper, we completely determine radio number of all transformation graphs of a path.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.2
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• pp.264-268
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• 2016

Recently, various energy efficiency optimization activities are ongoing globally by integrating conventional grids with ICT (Information and Communication Technology). In this sense, various smart grid projects, which power suppliers and consumers exchange useful informations bilaterally in real time, have been being carried out. The electric vehicle diffusion program is one of the projects and it has been spotlighted because it could resolve green gas problem, fuel economy and tightening environmental regulations. In this paper, the economics of V2G system which consists of electric vehicles and the charging infrastructure is evaluated comparing electric vehicles for V2G with common electric vehicles. Additional benefits of V2G are analyzed in the viewpoint of load leveling, frequency regulation and operation reserve. To find this benefit, electricity sales is modeled mathematically considering depth of discharge, maximum capacity reduction, etc. Benefit and cost analysis methods with the modeling are proposed to decide whether the introduction of V2G systems. Additionally, the methods will contribute to derive the future production and the unit cost of electric vehicle and battery and to get the technical and economic analysis.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.607-618
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• 2015

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.