• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.255-266
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• 2014

For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.

• 신재생에너지
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• 제9권4호
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• pp.19-24
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• 2013

In order to analyze the characteristics of tidal current power generation system, we measured output power in M-G Set (Motor-Generator Set) and MATLAB/Simulink. We installed M-G Set (Motor-Generator Set) and did a simulation using MATLAB/Smulink. The simulation consisted of the tidal current turbine, PMSG, converter, and three-phase PWM inverter. Also, the speed control of the generator was performed using machine side converter. And we measured output voltage, current, power of the generator and the output power of three-phase PWM inverter.

• 한국정보과학회논문지:시스템및이론
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• 제35권2호
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• pp.60-65
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• 2008

그래프의 매칭 배제 집합은 그것을 삭제한 그래프가 완전 매칭이나 준완전 매칭을 가지지 않는 에지 집합이다. 매칭 배제수는 모든 매칭 배제 집합의 최소 크기이다. 이 논문에서는 임의의 $m{\geq}4$에 대하여 H-차원 제한된 HL-그래프와 재귀원형군 $G(2^m,4)$의 매칭 배제수는 분지수 m과 같고, 모든 최소 매칭 배제 집합은 한 정점에 인접한 에지 집합임을 보인다.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.511-520
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• 2024

In this paper, we introduce the concept of split and non-split tree (D, C)- set of a connected graph G and its associated color variable, namely split tree (D, C) number and non-split tree (D, C) number of G. A subset S ⊆ V of vertices in G is said to be a split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is disconnected. The minimum size of the split tree (D, C) set of G is the split tree (D, C) number of G, γ_χST (G) = min{|S| : S is a split tree (D, C) set}. A subset S ⊆ V of vertices of G is said to be a non-split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is connected and non-split tree (D, C) number of G is γ_χST (G) = min{|S| : S is a non-split tree (D, C) set of G}. The split and non-split tree (D, C) number of some standard graphs and its compliments are identified.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.589-597
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• 2018

For $A,B{\in}M_2(\mathbb{C})$, let the Jordan product be AB + BA and G(A) the eigenvalue inclusion set, the Gershgorin set of A. Characterization is obtained for maps ${\phi}:M_2(\mathbb{C}){\rightarrow}M_2(\mathbb{C})$ satisfying $$G[{\phi}(A){\phi}(B)+{\phi}(B){\phi}(A)]=G(AB+BA)$$ for all matrices A and B. In fact, it is shown that such a map has the form ${\phi}(A)={\pm}(PD)A(PD)^{-1}$, where P is a permutation matrix and D is a unitary diagonal matrix in $M_2(\mathbb{C})$.

• International Journal of Fluid Machinery and Systems
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• 제1권1호
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• pp.10-23
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• 2008

The development of pre-set wavelength G$\ddot{o}$rtler vortices are studied in the boundary-layer flows on concave surfaces of 1.0 and 2.0 m radius of curvature. The wavelengths of the vortices were pre-set by thin wires of 0.2 mm diameter placed 10 mm upstream and perpendicular to the concave surface leading edge. Velocity contours were obtained from velocity measurements using a single hot-wire anemometer probe. The most amplified or dominant wavelength is found to be 15 mm for free-stream velocity of 2.1 m/s and 3.0 m/s on the concave surface of R = 1 m and 2 m, respectively. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different regions can be identified based on the growth rate of the vortices. The occurrence of a secondary instability mode is also shown in the form of mushroom-like structures as a consequence of the non-linear growth of the G$\ddot{o}$rtler vortices. By pre-setting the vortex wavelength to be much larger and much smaller than the most amplified one, the splitting and merging of G$\ddot{o}$rtler vortices can be respectively observed.

• Kyungpook Mathematical Journal
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• 제51권3호
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• pp.323-338
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• 2011

In this paper, we introduce ($$\tilde{g}$$, s)-continuous functions between topological spaces, study some of its basic properties and discuss its relationships with other topological functions.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• 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 $x\;{\in}\;V(G)$.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제5권
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• pp.523-523
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• 1997

Suppose that G is a group of permutations of a set ${\Omega}$. For a finite subset ${\gamma}$of${\Omega}$, the movement of ${\gamma}$ under the action of G is defined as move(${\gamma}$):=$max\limits_{g{\epsilon}G}|{\Gamma}^{g}{\backslash}{\Gamma}|$, and ${\gamma}$ will be said to have restricted movement if move(${\gamma}$)<|${\gamma}$|. Moreover if, for an infinite subset ${\gamma}$of${\Omega}$, the sets|{\Gamma}^{g}{\backslash}{\Gamma}| are finite and bounded as g runs over all elements of G, then we may define move(${\gamma}$)in the same way as for finite subsets. If move(${\gamma}$)${\leq}$m for all ${\gamma}$${\subseteq}$${\Omega}$, then G is said to have bounded movement and the movement of G move(G) is defined as the maximum of move(${\gamma}$) over all subsets ${\gamma}$ of ${\Omega}$. Having bounded movement is a very strong restriction on a group, but it is natural to ask just which permutation groups have bounded movement m. If move(G)=m then clearly we may assume that G has no fixed points is${\Omega}$, and with this assumption it was shown in [4, Theorem 1]that the number t of G=orbits is at most 2m-1, each G-orbit has length at most 3m, and moreover|${\Omega}$|${\leq}$3m+t-1${\leq}$5m-2. Moreover it has recently been shown by P. S. Kim, J. R. Cho and C. E. Praeger in [1] that essentially the only examples with as many as 2m-1 orbits are elementary abelian 2-groups, and by A. Gardiner, A. Mann and C. E. Praeger in [2,3]that essentially the only transitive examples in a set of maximal size, namely 3m, are groups of exponent 3. (The only exceptions to these general statements occur for small values of m and are known explicitly.) Motivated by these results, we would decide what role if any is played by primes other that 2 and 3 for describing the structure of groups of bounded movement.