• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.155-163
• /
• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Industrial Engineering and Management Systems
• /
• v.10 no.3
• /
• pp.221-231
• /
• 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
• /
• v.22 no.6
• /
• pp.1275-1281
• /
• 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.

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

• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.103-110
• /
• 2007

The purpose of this paper is to introduce the concept of fuzzy set connected functions and investigate their properties.

• ETRI Journal
• /
• v.38 no.5
• /
• pp.885-895
• /
• 2016

The lowest power mode (passive-standby mode) was proposed for reducing the power consumption of set-top boxes in a standby state when not receiving content. However, low-power set-top boxes equipped with the lowest power mode have been rarely commercialized because of their low-quality user experience. In the lowest power mode, they deactivates almost all of operational modules and processes, and thus require dozens of seconds for activation latency (that is, the latency for activating all modules of the set-top boxes in a standby state). They are not even updated in a standby state because they deactivate their network interfaces in a standby state. This paper proposes an adaptive standby mode scheduling method for improving the user experience of such boxes. Set-top boxes using the proposed method can analyze the activation pattern and find the frequently used time period (that is, when the set-top boxes are frequently activated). They prepare for their activation during this frequently used time period, thereby reducing the activation latency and enabling their update in a standby state.

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

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

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.6
• /
• pp.2619-2643
• /
• 2018

In this paper, a new clustering algorithm based on the connected region generation (CRG-clustering) is proposed. It is an effective and robust approach to clustering on the basis of the connectivity of the points and their neighbors. In the new algorithm, a connected region generating (CRG) algorithm is developed to obtain the connected regions and an isolated point set. Each connected region corresponds to a homogeneous cluster and this ensures the separability of an arbitrary data set theoretically. Then, a region expansion strategy and a consensus criterion are used to deal with the points in the isolated point set. Experimental results on the synthetic datasets and the real world datasets show that the proposed algorithm has high performance and is insensitive to noise.

• Journal of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.847-856
• /
• 2005

M. Junger, G. Reinelt, and W. R. Pulleyblank asked the following questions ([2]). (1) Is it true that every simple planar 2-edge connected bipartite graph has a 3-partition in which each component consists of the edge set of a simple path? (2) Does every simple planar 2-edge connected graph have a 3-partition in which every component consists of the edge set of simple paths and triangles? The purpose of this paper is to provide a positive answer to the second question for simple outerplanar 2-vertex connected graphs and a positive answer to the first question for simple planar 2-edge connected bipartite graphs one set of whose bipartition has at most 4 vertices.