• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.41-46
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• 2016

A graph G of order n has prime cordial labeling if its vertices can be assigned the distinct labels 1, $2{\cdots}$, n such that if each edge xy in G is assigned the label 1 in case the labels of x and y are relatively prime and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we give a complete characterization of complete graphs which are prime cordial and we give a prime cordial labeling of the closed helm ${\bar{H}}_n$, and present a new way of prime cordial labeling of $P^2_n$. Finally we make a correction of the proof of Theorem 2.5 in [12].

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.285-294
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• 2021

In the present work we introduce Gaussian vertex prime labeling and investigate Gaussian vertex prime labeling for gear graph, book graph, wheel graph, kayak paddle, one point union of gear graph and one point union of wheel graph.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.149-156
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• 2019

Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.

• Journal of the Korea Society of Computer and Information
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• v.12 no.5
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• pp.65-72
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• 2007

Labeling schemes which don't consider about frequent update in dynamic XML documents need relabeling process to reflect the changed label information whenever the tree of XML document is update. There is disadvantage of considerable expenses in the dynamic XML document which can occurs frequent update. To solve this problem, we suggest prime number labeling scheme that doesn't need relabeling process. However the prime number labeling scheme does not consider that it needs to update the sibling order of nodes in the tree of XML document. This update process needs much costs because the most of the tree of XML document has to be researched and rewritten. In this paper, we propose the prime number labeling scheme with sibling order value that can maintain the sibling order without researching or rewriting the tree of XML documents.

• Journal of KIISE:Databases
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• v.33 no.1
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• pp.129-137
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• 2006

An XML labeling scheme is an efficient encoding method to determine the ancestor-descendant relationships of elements and the orders of siblings. Recently, many dynamic XML documents have appeared in the Web Services and the AXML(the Active XML), so we need to manage them with a dynamic XML labeling scheme. The prime number labeling scheme is a representative scheme which supports dynamic XML documents. It determines the ancestor-descendant relationships between two elements with the feature of prime numbers. When a new element is inserted into the XML document using this scheme, it has an advantage that an assigning the label of new element don't change the label values of existing nodes. But it has to have additional expensive operations and data structure for maintaining the orders of siblings. In this paper, we suggest the order number sharing method and algorithms categorized by the insertion positions of new nodes. They greatly minimize the existing method's sibling order maintenance cost.

• Journal of KIISE:Databases
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• v.36 no.3
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• pp.180-188
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• 2009

Recently, the needs for an efficient and secure access control method of dynamic XML data in a ubiquitous data streams environment have become an active research area. In this paper, we proposed an improved role-based prime number labeling scheme for an efficient and secure access control labeling method in dynamic XML data streams. And we point out the limitations of existing access control and labeling schemes for XML data assuming that documents are frequently updated. The improved labeling method where labels are encoded ancestor-descendant and sibling relationships between nodes but need not to be regenerated when the document is updated. Our improved role-based prime number labeling scheme supports an infinite number of updates and guarantees the arbitrary nodes insertion at arbitrary position of the XML tree without label collisions. Also we implemented an efficient access control using a role-based prime number labeling. Finally, we have shown that our approach is an efficient and secure through experiments.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.12
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• pp.2219-2225
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• 2008

Labeling schemes which don't consider about frequent update in dynamic XML documents need relabeling process to reflect the changed label information whenever the tree of XML document is update. There is disadvantage of considerable expenses in the dynamic XML document which can occurs frequent update. To solve this problem, we suggest prime number labeling scheme that doesn't need relabeling process. However the prime number labeling scheme does not consider that it needs to update the sibling order of nodes in the XML tree of document. This update process needs much costs because the most of the XML tree of document has to be relabeling and recalculation. In this paper, we propose the prime number labeling scheme with sibling order value that can maintain the sibling order without relabeling or recalculation the XML tree of documents.

• Journal of KIISE
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• v.41 no.9
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• pp.699-706
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• 2014

As XML documents are getting bigger and more complex, a keyword-based search method that does not require structural information is needed to search these large XML documents. In order to use this method, not only all keywords expressed as nodes in the XML document must be labeled for indexing but also structural information should be well represented. However, the existing labeling methods either have very simple information of XML documents for index or represent the structural information which is difficult to deal with the increase of XML documents' size. As the size of XML documents is getting larger, it causes either the poor performance of keyword search or the exponential increase of space usage. In this paper, we present the Repetitive Prime Labeling Scheme (RPLS) in order to improve the problem of the existing labeling methods for keyword-based search of large XML documents. This method is based on the existing prime number labeling method and allows a parent's prime number to be used at a lower level repeatedly so that the number of prime numbers being generated can be reduced. Then, we show an experimental result of the comparison between our methods and the existing methods.

• Journal of the Korea Society of Computer and Information
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• v.16 no.4
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• pp.169-177
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• 2011

As demand for efficiency in handling dynamic XML data grows, new dynamic XML labeling schemes have been researched. The key idea of the dynamic XML labeling scheme is to find ancestor-descendent-sibling relationships and to minimize memory space to store total label, response time and range of relabeling incurred by update operations. The prime number labeling scheme is a representative scheme which supports dynamic XML documents. It determines the ancestor-descendant relationships between two elements by a simple divisibility test of labels. When a new element is inserted into the XML data using this scheme, it does not change the label values of existing nodes. However, since each prime number must be used exclusively, labels can become significantly large. Therefore, in this paper, we introduce a novel technique to effectively reduce the problem of label overflow. The suggested idea is based on tree decomposition. When label overflow occurs, the full tree is divided into several sub-trees, and nodes in each sub-tree are separately labeled. Through experiments, we show the effectiveness of our scheme.