• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.41-53
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• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.1-14
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• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• Proceedings of the IEEK Conference
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• 2001.06d
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• pp.231-234
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• 2001

This paper proposes a face recognition technique that effectively combines elastic graph matching (EGM) and Fisherface algorithm. EGM as one of dynamic lint architecture uses not only face-shape but also the gray information of image, and Fisherface algorithm as a class specific method is robust about variations such as lighting direction and facial expression. In the proposed face recognition adopting the above two methods, the linear projection per node of an image graph reduces dimensionality of labeled graph vector and provides a feature space to be used effectively for the classification. In comparison with a conventional method, the proposed approach could obtain satisfactory results in the perspectives of recognition rates and speeds. Especially, we could get maximum recognition rate of 99.3% by leaving-one-out method for the experiments with the Yale Face Databases.

• Journal of Communications and Networks
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• v.15 no.4
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• pp.407-410
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• 2013

Secret sharing is that a dealer distributes a piece of information (called a share) about a secret to each participant such that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. In this paper, an access structure can be represented by a label graph G, where a vertex denotes a participant and a complete subgraph of G corresponds to a minimal authorized subset. The vertices of G are labeled into distinct vectors uniquely determined by the maximum prohibited structure. Based on such a label graph, a verifiable secret sharing scheme realizing general access structures is proposed. A major advantage of this scheme is that it applies to any access structure, rather than only structures representable as previous graphs, i.e., the access structures of rank two. Furthermore, verifiability of the proposed scheme can resist possible internal attack performed by malicious participants, who want to obtain additional shares or provide a fake share to other participants.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.557-584
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• 2024

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tⁿ ≃ (S¹)ⁿ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χ_y-genus of M.

• Journal of KIISE
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• v.42 no.12
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• pp.1561-1567
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• 2015

Abstract Semi-supervised learning is an area in machine learning that employs both labeled and unlabeled data in order to train a model and has the potential to improve prediction performance compared to supervised learning. Graph-based semi-supervised learning has recently come into focus with two phases: graph construction, which converts the input data into a graph, and label inference, which predicts the appropriate labels for unlabeled data using the constructed graph. The inference is based on the smoothness assumption feature of semi-supervised learning. In this study, we propose an enhanced label inference algorithm by incorporating the importance of each vertex. In addition, we prove the convergence of the suggested algorithm and verify its excellence.

• KIPS Transactions on Computer and Communication Systems
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• v.12 no.5
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• pp.165-170
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• 2023

With the recent rise of blockchain technology, cryptocurrency platforms using it are increasing, and currency transactions are being actively conducted. However, crimes that abuse the characteristics of cryptocurrency are also increasing, which is a problem. In particular, phishing scams account for more than a majority of Ethereum cybercrime and are considered a major security threat. Therefore, effective phishing scams detection methods are urgently needed. However, it is difficult to provide sufficient data for supervised learning due to the problem of data imbalance caused by the lack of phishing addresses labeled in the Ethereum participating account address. To address this, this paper proposes a phishing scams detection method that uses both Trans2vec, an effective graph embedding techique considering Ethereum transaction networks, and semi-supervised learning model Tri-training to make the most of not only labeled data but also unlabeled data.

• Journal of KIISE:Databases
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• v.29 no.4
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• pp.274-284
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• 2002

Queries on XML are based on paths in the data graph, which is represented as an edge labeled graph model. All proposed query languages for XML express queries using regular expressions to traverse arbitrary paths in the data graph. A meaningful query usually has several regular path expressions in it, but much of recent research is more concerned with optimizing a single path expression. In this paper, we present an efficient technique to process multiple path expressions in a query. We developed a data structure named as the path identifier(PID) to identify whether two given nodes lie on the fame path in the data graph or not, and utilized the PID for efficient processing of multiple path expressions. We implement our technique and present preliminary performance results.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.