Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding

Zhang, Xiaohui; Ye, Chengfu; Zhang, Shumin; Yao, Bing

doi:10.3390/math10091592

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…Topological coding is related to NP problems in graph theory and operations research, as well as many mathematical conjectures, making it computationally unbreakable or provable in terms of security. Since topological graphic passwords are related with many mathematical conjectures and NP-hard problems, so topological graphic passwords are computationally unbreakable or provable security, and the investigation of topological graphic passwords have been introduced in these articles [2,3,4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding

Zhang

Yao

2023

Preprint

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We use topological graphs to generate topological coding, which is a fundamental technology in number theory, algebra, and has potential application value in asymmetric encryption systems. This article proposes a method of using topological graph sequences to generate topological coding for protecting hash ciphers, which can effectively protect hash ciphers even in the event of password leakage. We use topology graphs with labelings and colorings to generate graph lattice, which is the application of graph markers in asymmetric encryption systems. There are various kinds of graph labeling, one of them is a harmonious labeling. In order to further study topological coding, we use the graph harmonious-type labelings and colorings to propose (k, d)-harmonious labelling , since they can be applied to build up a new approach of asymmetric encryption. Finally, several typical attack methods about graph lattice analyzed to verify the effectiveness of our scheme.

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Section: Introductionmentioning

confidence: 99%

Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding

Zhang

Yao

2023

Preprint

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Efficient Graph Network Using Total Magic Labeling and Its Applications

Meenakshi,

Kannan,

Cep

et al. 2023

Mathematics

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Cryptography is a pivotal application of graph theory in ensuring secure communication systems. Modern cryptography is deeply rooted in mathematical theory and computer science practices. It is widely recognized that encryption and decryption processes are primarily outcomes of mathematical research. Given the increasing importance of safeguarding secret information or messages from potential intruders, it is imperative to develop effective technical tools for this purpose. These intruders are often well-versed in the latest technological advancements that could breach security. To address this, our study focuses on the efficacious combinatorial technique of graph networks using efficient domination and total magic labeling. The introduction of a graph network based on total magic labeling can significantly influence the network’s performance. This research introduces a novel combinatorial method for encrypting and decrypting confidential numbers by leveraging an efficient dominant notion and labeled graph.

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The connection between the magical coloring of trees

Su,

Zhang,

Yao

2024

MATH

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<p>Let $ f $ be a set-ordered edge-magic labeling of a graph $ G $ from $ V(G) $ and $ E(G) $ to $ [0, p-1] $ and $ [1, p-1] $, respectively; it also satisfies the following conditions: $ |f(V(G))| = p $, $ \max f(X) < \min f(Y) $, and $ f(x)+f(y)+f(xy) = C $ for each edge $ xy\in E(G) $. In this paper, we removed the restriction that the labeling of vertices could not be repeated, and presented the concept of magical colorings including edge-magic coloring, edge-difference coloring, felicitous-difference coloring, and graceful-difference coloring. We studied the magical colorings on the tree and proved the existence of four kinds of magical colorings on the tree from a set-ordered edge-magic labeling. Further, we revealed the transformation relationship between these kinds of colorings.</p>

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Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding

Cited by 3 publications

References 10 publications

Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding

Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding

Efficient Graph Network Using Total Magic Labeling and Its Applications

The connection between the magical coloring of trees

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