• Industrial Engineering and Management Systems
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• v.10 no.3
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• pp.221-231
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• 2011

One of the critical issues in wireless sensor network is the design of a proper routing protocol. One possible approach is utilizing a virtual infrastructure, which is a subset of sensors to connect all the sensors in the network. Among the many virtual infrastructures, the connected dominating set is widely used. Since a small connected dominating set can help to decrease the protocol overhead and energy consumption, it is preferable to find a small sized connected dominating set. Although many algorithms have been suggested to construct a minimum connected dominating set, there have been few exact approaches. In this paper, we suggest an improved optimal algorithm for the minimum connected dominating set problem, and extensive computational results showed that our algorithm outperformed the previous exact algorithms. Also, we suggest a new heuristic algorithm to find the connected dominating set and computational results show that our algorithm is capable of finding good quality solutions quite fast.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1275-1281
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• 2011

Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition, we give a polynomial time algorithm for determining the balancedness of the game on a tree, for finding a element of the core.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.5B
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• pp.274-286
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• 2005

In this paper, we propose a new power-efficient and reliable connected dominating set based routing protocol in the mobile ad hoc networks. Gateway nodes must be elected in consideration of residual energy and mobility because frequent reconstruction of connected dominating set result in transmission error for route losses. If node density is high, it results in a lot of contentions and more delays for network congestion. Therefore, in this paper, we propose a new construction method of connected dominating set that supports reliable and efficient data transmission through minimizing reconstruction of connected dominating set by delaying neighbor set advertisement message broadcast in proportion to weighted sum of residual energy, mobility, and the number of neighbor nodes. The performance of the proposed protocol is proved by simulation of various conditions.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.1-12
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• 2021

A dominating set S of a graph G is said to be nonsplit dominating set if the subgraph ⟨V - S⟩ is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number and is denoted by ��ns(G). For a minimum nonsplit dominating set S of G, a set T ⊆ S is called a forcing subset for S if S is the unique ��ns-set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing nonsplit domination number of S, denoted by f��ns(S), is the cardinality of a minimum forcing subset of S. The forcing nonsplit domination number of G, denoted by f��ns(G) is defined by f��ns(G) = min{f��ns(S)}, where the minimum is taken over all ��ns-sets S in G. The forcing nonsplit domination number of certain standard graphs are determined. It is shown that, for every pair of positive integers a and b with 0 ≤ a ≤ b and b ≥ 1, there exists a connected graph G such that f��ns(G) = a and ��ns(G) = b. It is shown that, for every integer a ≥ 0, there exists a connected graph G with f��(G) = f��ns(G) = a, where f��(G) is the forcing domination number of the graph. Also, it is shown that, for every pair a, b of integers with a ≥ 0 and b ≥ 0 there exists a connected graph G such that f��(G) = a and f��ns(G) = b.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.361-369
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• 2018

For a given graph G = (V, E), a set $D{\subseteq}V(G)$ is said to be an outer-connected vertex edge dominating set if D is a vertex edge dominating set and the graph $G{\backslash}D$ is connected. The outer-connected vertex edge domination number of a graph G, denoted by ${\gamma}^{oc}_{ve}(G)$, is the cardinality of a minimum outer connected vertex edge dominating set of G. We characterize trees T of order n with l leaves, s support vertices, for which ${\gamma}^{oc}_{ve}(T)=(n-l+s+1)/3$ and also characterize trees with equal domination number and outer-connected vertex edge domination number.

• Journal of applied mathematics & informatics
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• v.41 no.4
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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.

• Proceedings of the Korea Information Processing Society Conference
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• 2005.05a
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• pp.1493-1496
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• 2005

연결형 dominating set기반의 라우팅 알고리즘에서 잦은 dominating set의 재구성은 루트 손실로 인한 전송 에러를 발생시키기 때문에, 노드의 잔여 전력량과 이동성을 고려하여 게이트웨이 노드를 선택하여야 한다. 또한 같은 지역에 노드가 집중되어 있다면 매체를 공유하는 무선 네트워크의 특성상 병목으로 인한 충돌 및 지연 등이 야기 될 가능성이 크다. 따라서 본 논문에서는 노드의 잔여 전력량 및 이동성, 이웃 노드수의 가중 가산 값에 비례하여 이웃 구성 통보 메시지 (neighbor set advertisement message)의 브로드캐스팅을 지연시키는 방법을 통해 연결형 dominating set의 재구성을 최소화 하여 신뢰성 있고 효율적인 데이터 전송을 보장하는 새로운 연결형 dominating set 구성 방법을 제안하고 다양한 상황에서의 실험을 통해 그 성능을 비교 평가하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.12A
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• pp.1188-1197
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• 2010

A most important thing in a connected dominating set(CDS)-based routing in a wireless ad-hoc network is to select a minimum number of dominating nodes and then build a backbone network which is made of them. Node failure in a CDS is an event of non-negligible probability. For applications where fault tolerance is critical, a traditional dominating-set based routing may not be a desirable form of clustering. It is necessary to minimize the frequency of reconstruction of a CDS to reduce message overhead due to message flooding. The idea is that by finding alternative nodes within a restricted range and locally reconstructing a CDS to include them, instead of totally reconstructing a new CDS. With the proposed algorithm, the resulting number of dominating nodes after partial reconstruction of CDS is not changed and also its execution time is faster than well-known algorithm of construction of CDS by 20~40%. In the case of high mobility situation, the proposed algorithm gives better results for the performance metrics, packet receive ratio and energy consumption.

• The Journal of the Korea Contents Association
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• v.9 no.8
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• pp.49-56
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• 2009

In this paper, we propose a method of energy level, node degree and selection information based CDS(Connected Dominating Set) construction algorithm for more efficient routing in ad-hoc wireless networks. Constructing CDS in ad-hoc wireless network, it is necessary to make more efficient algorithm that is faster, more simple and has low power consumption. A CDS must be minimized because nodes in the CDS consume more energy in order to handle various bypass traffics than nodes outside the set. It is better not to reconstruct CDS after constructing the most efficient CDS. To overcome this problem, we proposed the CDS construction algorithms based on EL+ND+Sel method. We compared and estimated the performance in each situation of EL + ND and EL + ND + Sel.