• Journal of applied mathematics & informatics
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• v.42 no.3
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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.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.37-44
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• 1999

We study the relations among the domination number, the independent domination number, and the independence number of an oriented tree and establish their bounds. We also do the same for a binary tree.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.245-250
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• 2020

Let γt(G) and τ(G) denote the total domination number and vertex cover number of graph G, respectively. In this paper, we study the total domination number of the central tree C(T) for a tree T. First, a relationship between the total domination number of C(T) and the vertex cover number of tree T is discussed. We characterize the central trees with equal total domination number and independence number. Applying the first result, we improve the upper bound on the total domination number of C(T) and solve one open problem posed by Kazemnejad et al..

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.2
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• pp.121-125
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• 2008

It is essential to maintain hierarchical information properly for efficient XML query processing. Well known approach to represent hierarchical information of XML tree is assigning a specific node number to each node of XML tree. Insertion and deletion of XML node can occur at any position in a dynamic XML tree. A dynamic numbering scheme allows us to add nodes to or delete nodes from an XML tree without relabeling or with relabeling only a few existing nodes of XML tree while executing XML query efficiently. According to W3C XQuery update facility specifications a node can be added as first or last child of the existing node in XML tree. Generating new number for last child requires referencing the number of previous last child. Getting the number of last child is very costly with previous approaches. We have developed a new dynamic numbering scheme PSN which is very effective for insertion of a node as last child. Our approach reduces the time to find last child dramatically by removing sorting of children.

• Journal of KIISE:Databases
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• v.31 no.3
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• pp.252-260
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• 2004

Recently, the TPR-tree has been proposed to support spatio-temporal queries for moving objects. Subsequently, various methods using the TPR-tree have been intensively studied. However, although the TPR-tree is one of the most popular access methods in spatio-temporal databases, any cost model for the TPR-tree has not yet been proposed. Existing cost models for the spatial index such as the R-tree do not accurately ostinato the number of disk accesses for spatio-temporal queries using the TPR-tree, because they do not consider the future locations of moving objects. In this paper, we propose a cost model of the TPR-tree for moving objects for the first time. Extensive experimental results show that our proposed method accurately estimates the number of disk accesses over various spatio-temporal queries.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Journal of Information Technology and Architecture
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• v.9 no.1
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• pp.11-19
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• 2012

Generally, a suffix tree is an efficient data structure since it reveals the detailed internal structures of given sequences within linear time. However, it is difficult to implement a suffix tree for a large number of sequences because of memory size constraints. Therefore, in order to compare multi-mega base genomic sequence sets using suffix trees, there is a need to re-construct the suffix tree algorithms. We introduce a new method for constructing a suffix tree on secondary storage of a large number of sequences. Our algorithm divides three files, in a designated sequence, into parts, storing references to the locations of edges in hash tables. To execute experiments, we used 1,300,000 sequences around 300Mbyte in EST to generate a suffix tree on disk.

• Industrial Engineering and Management Systems
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• v.4 no.1
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• pp.102-108
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• 2005

This paper studies medical data classification methods, comparing decision tree and system reconstruction analysis as applied to heart disease medical data mining. The data we study is collected from patients with coronary heart disease. It has 1,723 records of 71 attributes each. We use the system-reconstruction method to weight it. We use decision tree algorithms, such as induction of decision trees (ID3), classification and regression tree (C4.5), classification and regression tree (CART), Chi-square automatic interaction detector (CHAID), and exhausted CHAID. We use the results to compare the correction rate, leaf number, and tree depth of different decision-tree algorithms. According to the experiments, we know that weighted data can improve the correction rate of coronary heart disease data but has little effect on the tree depth and leaf number.

• Journal of Environmental Science International
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• v.19 no.9
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• pp.1129-1136
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• 2010

This study investigated the status of planting status of school's flower of 11 elementary schools located in Chung-ju and its results were as follows. Totally 3,502 trees were planted in the 11 schools and the number of species of the trees was 103. For tall tree Thuja orientalis was planted most frequently and for shrub Buxus microphylla was done in the largest number of the schools. In addition, the number of trees planted in a school was averagely two times more in the model schools than in the other ones, and the average number of species of trees was also over three times more in the model schools. When the number of species of trees was examined according to their types, decidous broad leaved tree was found most frequently overall and the model schools had more various species of decidous tree compared to the other ones. Investigation on designation of school's flower and tree with the 11 elementary school, revealed similar results with those of previous studies performed with the schools in other areas and the tendency meant that the designation was uniform to some degree. Moreover, as only a few school's flower and tree were planted or no one was done in some schools, the species of school's flower and tree needed to be determined by considering characteristics and school percepts of a school as well as local features and circumstances of a region. In addition, more efforts should be made to infuse love for school and to improve quality of education by increasing the planting rate of school's flower and tree and by focusing them.