• 대한수학회보
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• 제47권6호
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• pp.1155-1162
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• 2010

In this paper, we find the maximum exponent of D ${\times}$ E, the cartesian product of two digraphs D and E on n, n + 2 vertices, respectively for an even integer $n\geq4$. We also characterize the extrema cases.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.279-287
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• 2015

A subset S of V (G), where G is a graph without isolated vertices, is a double dominating set of G if for each $x{{\in}}V(G)$, ${\mid}N_G[x]{\cap}S{\mid}{\geq}2$. This paper, shows that any positive integers a, b and n with $2{\leq}a<b$, $b{\geq}2a$ and $n{\geq}b+2a-2$, can be realized as domination number, double domination number and order, respectively. It also characterize the double dominating sets in the Cartesian and tensor products of two graphs and determine sharp bounds for the double domination numbers of these graphs. In particular, it show that if G and H are any connected non-trivial graphs of orders n and m respectively, then ${\gamma}_{{\times}2}(G{\square}H){\leq}min\{m{\gamma}_2(G),n{\gamma}_2(H)\}$, where ${\gamma}_2$, is the 2-domination parameter.

• Korean Journal of Mathematics
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• 제2권
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• pp.73-77
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• 1994

• Korean Journal of Mathematics
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• 제25권2호
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• pp.279-301
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• 2017

An L(3, 2, 1)-labeling for the graph G = (V, E) is an assignment f of a label to each vertices of G such that ${\mid}f(u)-f({\upsilon}){\mid}{\geq}4-k$ when $dist(u,{\upsilon})=k{\leq}3$. The L(3, 2, 1)-labeling number, denoted by ${\lambda}_{3,2,1}(G)$, for G is the smallest number N such that there is an L(3, 2, 1)-labeling for G with span N. In this paper, we compute the L(3, 2, 1)-labeling number ${\lambda}_{3,2,1}(G)$ when G is a cylindrical grid, which is the cartesian product $P_m{\Box}C_n$ of the path and the cycle, when $m{\geq}4$ and $n{\geq}138$. Especially when n is a multiple of 4, or m = 4 and n is a multiple of 6, then we have ${\lambda}_{3,2,1}(G)=11$. Otherwise ${\lambda}_{3,2,1}(G)=12$.

• 충청수학회지
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• 제30권2호
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• pp.213-226
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• 2017

The concept of fuzzy transitive filters is introduced in BE-algebras. Some sufficient conditions are established for every fuzzy filter of a BE-algebra to become a fuzzy transitive filter. Some properties of fuzzy transitive filters are studied with respect to fuzzy relations and cartesian products.

• 한국멀티미디어학회:학술대회논문집
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• 한국멀티미디어학회 1998년도 추계학술발표논문집
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• pp.202-207
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• 1998

The network reliability is to be computed in terms of the terminal reliability. The computation of a terminal reliability is started with a Boolean sum of products expression corresponding to simple paths of the pair of nodes. This expression is then transformed into another equivalent expression to be a Disjoint Sum of Products form. But this computation of the terminal reliability obviously does not consider the communication between any other nodes but for the source and the sink. In this paper, we derive the overall network reliability which all other remaining nodes. For this, we propose a method to make the SOP disjoint for deriving the network reliability expression from the system success expression using the modified Sheinman's method. Our method includes the concept of spanning trees to find the system success function by the Cartesian products of vertex cutsets.

• 한국주조공학회지
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• 제43권6호
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• pp.302-309
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• 2023

일반적으로 주조품은 복잡한 형상을 가지고 있고, 한 제품 내에서 두께의 차이가 현저하게 나는 경우가 있어 시뮬레이션을 위한 격자를 생성할 때 어려움이 있다. 주조 유동은 이상유동으로 수치해석을 할 때 공기와 용탕의 경계면을 추적해야하며 밀도차에 의한 압력장 계산에 많은 시간이 소요된다. 이와 같은 이유로 주조유동해석에는 직교격자가 주로 이용되어왔다. 그러나 직교격자는 형상을 제대로 표현하지 못한다. 곡면에서 나타나는 계단형상 격자로 인해 모멘텀 손실이 발생하고 이로 인해 용탕의 흐름이 달라질 수 있으며 결과적으로 잘못된 주조 방안 설계를 할 수 있다. 이를 피하기 위하여 직교격자계에서 형상을 좀 더 정확하게 표현하기 위하여 많은 수의 격자를 생성하여 해석을 한다. 또는 직교격자계에서 발생하는 문제를 수치적으로 보완하는 Cut Cell 방법을 적용하여 해석하는 방법이 있다. 본 연구에서는 직교격자계에서 주조유동해석을 할 때 격자수에 따른 해석결과와 Cut Cell 방법을 적용한 해석 결과를 비교하였다. 또한 주조공정별로 실제제품을 주조유동해석을 하고 공정별로 Cut Cell 방법을 적용한 결과를 고찰하였다.

• 호남수학학술지
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• 제29권1호
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• pp.101-118
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• 2007

The notions of digital k-homotopy equivalence and digital ($k_0,k_1$)-homotopy equivalence were developed in [13, 16]. By the use of the digital k-homotopy equivalence, we can investigate digital k-homotopy equivalent properties of Cartesian products constructed by the minimal simple closed 4- and 8-curves in $\mathbf{Z}^2$.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.175-190
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• 2019

In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.

• 호남수학학술지
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• 제37권1호
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• pp.135-147
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• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.