• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.839-848
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• 2023

Let G be a simple undirected graph. A planar graph known as a Halin graph(HG) is characterised by having three connected and pendent vertices of a tree that are connected by an outer cycle. A subset S of V is said to be a dominating set of the graph G if each vertex u that is part of V is dominated by at least one element v that is a part of S. The domination number of a graph is denoted by the γ(G), and it corresponds to the minimum size of a dominating set. A dominating set S is called a secure dominating set if for each v ∈ V＼S there exists u ∈ S such that v is adjacent to u and S₁ = (S＼{v}) ∪ {u} is a dominating set. The minimum cardinality of a secure dominating set of G is equal to the secure domination number γ_s(G). In this article we found the secure domination number of Halin graph(HG) with perfet k-ary tree and also we determined secure domination of rooted product of special trees.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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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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• 제14권1_2호
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• pp.185-191
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• 2004

Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

• Kyungpook Mathematical Journal
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• 제16권2호
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• pp.243-246
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• 1976

• Kyungpook Mathematical Journal
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• 제11권2호
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• pp.169-172
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• 1971

• 충청수학회지
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• 제20권3호
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• pp.343-348
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• 2007

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

• 충청수학회지
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• 제23권4호
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• 한국지능시스템학회논문지
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• 제16권6호
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• pp.683-690
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• 2006

무선 센서 네트워크에서 에너지 소비의 효율성은 전체 네트워크 수명 시간을 결정하기 때문에 에너지 소비를 최소화하기 위한 연구가 활발히 진행되고 있다. 무선 센서 네트워크에서 에너지 보전을 위해서는 운영에 필요한 최소한 센서 노드만을 활성화된 상태로 유지하고 나머지 노드들은 휴면 상태로 유지하여 불필요한 에너지 소비가 일어나지 않도록 하여야 한다. 그러나 얼마만큼의 센서 노드들을 최적의 운영 노드 집합에 포함시킬 것인지를 계산하는 것은 NP-hard 문제로 알려져 있다. 본 논문에서는 최적에 근접한 커버 집합(cover set)을 생성하기 위하여 CVT 기반의 근사화 알고리즘을 제안하였다. 제안된 알고리즘에서는 센서의 통신 범위가 센싱 범위의 두 배 이상이면 커버 집합에 속한 센서 노드 간의 연결이 즉시 이루어지도록 하고 반면에 통신 범위가 센싱 범위의 두 배 이하이면 커버 집합의 접속성 보장을 위하여 보조 노드를 결정하는 연결 기법을 제시하였다. 마지막으로 제안된 알고리즘의 성능 평가를 위하여 이론적 분석과 실험을 수행하였으며, 실험결과를 통해 제안된 알고리즘이 Greedy 알고리즘보다 CCS(Connected Cover Set)의 크기와 실행 시간 측면에서 우수함을 보였다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.731-734
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• 1998

A scalable parallel algorithm is proposed for efficient image component labeling with local operatos on a mesh connected SIMD computer. In contrast to the conventional parallel labeling algorithms, where a single pixel is assigned to each PE, the algorithm presented here is scalable and can assign m$\times$m pixel set to each PE according to the input image size. The assigned pixel set is converted to a single pixel that has representative value, and the amount of the required memory and processing time can be highly reduced. For N$\times$N image, if m$\times$m pixel set is assigned to each PE of P$\times$P mesh, where P=N/m, the time complexity due to the communication of each PE and the computation complexity are reduced to O(PlogP) bit operations and O(P) bit operations, respectively, which is 1/m of each of the conventional method. This method also diminishes the amount of memory in each PE to O(P), and can decrease the number of PE to O(P2) =Θ(N2/m2) as compared to O(N2) of conventional method. Because the proposed parallel labeling algorithm is scalable, we can adapt to the increase of image size without the hardware change of the given mesh connected SIMD computer.

• 충청수학회지
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• 제28권1호
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• pp.139-143
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• 2015

In this paper, we prove that (r, s)-semi-irresolute image of the (r, s)-semi-${\theta}$-connected set is also (r, s)-semi-${\theta}$-connected. Moreover, we prove that an (r, s)-semi-irresolute mapping preserves (r; s)-$S^*$-closedness.