Bing Yao
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View article: Topological Structures of Sets and their Subsets
Topological Structures of Sets and their Subsets Open
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating hypergr…
View article: Random Generation Topology Coding Technique in Asymmetric Topology Encryption
Random Generation Topology Coding Technique in Asymmetric Topology Encryption Open
The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by qua…
View article: MUSE-Net: Missingness-aware mUlti-branching Self-attention Encoder for Irregular Longitudinal Electronic Health Records
MUSE-Net: Missingness-aware mUlti-branching Self-attention Encoder for Irregular Longitudinal Electronic Health Records Open
The era of big data has made vast amounts of clinical data readily available, particularly in the form of electronic health records (EHRs), which provides unprecedented opportunities for developing data-driven diagnostic tools to enhance c…
View article: The connection between the magical coloring of trees
The connection between the magical coloring of trees Open
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…
View article: Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding
Exploring Asymmetric Encryption of Harmonious-Type Labeling and Coloring Topological Coding Open
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 topologica…
View article: Graphic Groups, Graph Homomorphisms, and Graphic Group Lattices in Asymmetric Topology Cryptography
Graphic Groups, Graph Homomorphisms, and Graphic Group Lattices in Asymmetric Topology Cryptography Open
Using asymmetric topology cryptography to encrypt networks on the basis of topology coding is a new topic of cryptography, which consists of two major elements, i.e., topological structures and mathematical constraints. The topological sig…
View article: On Divided-Type Connectivity of Graphs
On Divided-Type Connectivity of Graphs Open
The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding grap…
View article: Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography
Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography Open
We, for anti-quantum computing, will discuss various number-based strings, such as number-based super-strings, parameterized strings, set-based strings, graph-based strings, integer-partitioned and integer-decomposed strings, Hanzi-based s…
View article: Adjusting the Trapping Process of a Directed Weighted Edge-Iteration Network
Adjusting the Trapping Process of a Directed Weighted Edge-Iteration Network Open
Controlling the trapping process is one of the important themes in the study of random walk in real complex systems. We studied two types of random walks that are different from the traditional random walk on a directed weighted network. T…
View article: Parameterized Colorings And Labellings Of Graphs In Topological Coding
Parameterized Colorings And Labellings Of Graphs In Topological Coding Open
The coming quantum computation is forcing us to reexamine the cryptosystems people use. We are applying graph colorings of topological coding to modern information security and future cryptography against supercomputer and quantum computer…
View article: Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding
Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding Open
With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topologic…
View article: New Techniques Based On Odd-Edge Total Colorings In Topological Cryptosystem
New Techniques Based On Odd-Edge Total Colorings In Topological Cryptosystem Open
For building up twin-graphic lattices towards topological cryptograph, we define four kinds of new odd-magic-type colorings: odd-edge graceful-difference total coloring, odd-edge edge-difference total coloring, odd-edge edge-magic total co…
View article: The Structure and First-Passage Properties of Generalized Weighted Koch Networks
The Structure and First-Passage Properties of Generalized Weighted Koch Networks Open
Characterizing the topology and random walk of a random network is difficult because the connections in the network are uncertain. We propose a class of the generalized weighted Koch network by replacing the triangles in the traditional Ko…
View article: Topological Authentication Technique In Topologically Asymmetric Cryptosystem
Topological Authentication Technique In Topologically Asymmetric Cryptosystem Open
Making topological authentication from theory to practical application is an important and challenging task. More and more researchers pay attention on coming quantum computation, privacy data protection, lattices and cryptography. Researc…
View article: Graph Set-colorings And Hypergraphs In Topological Coding
Graph Set-colorings And Hypergraphs In Topological Coding Open
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we wil…
View article: An extension on neighbor sum distinguishing total coloring of graphs
An extension on neighbor sum distinguishing total coloring of graphs Open
Let $f: V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ be a non-proper total $k$-coloring of $G$. Define a weight function on total coloring as $$\phi(x)=f(x)+\sum\limits_{e\ni x}f(e)+\sum\limits_{y\in N(x)}f(y),$$ where $N(x)=\{y\in V(G)|xy\in…
View article: Eigenvalues of transition weight matrix for a family of weighted networks
Eigenvalues of transition weight matrix for a family of weighted networks Open
In this article, we design a family of scale-free networks and study its random target access time and weighted spanning trees through the eigenvalues of transition weight matrix. First, we build a type of fractal network with a weight fac…
View article: On Elegant Labelling and Magic Labelling of Large‐Scale Graphs
On Elegant Labelling and Magic Labelling of Large‐Scale Graphs Open
In this paper, we deduce the equivalence relationship among strongly c‐elegant labelling, super‐edge magic total labelling, edge antimagic total labelling, and super ( t , 1)‐magical labelling. We study some properties of the graph with a …
View article: Neighbor full sum distinguishing total coloring of Halin graphs
Neighbor full sum distinguishing total coloring of Halin graphs Open
Let $ f: V(G)\cup E(G)\rightarrow \{1, 2, \dots, k\} $ be a total $ k $ -coloring of $ G $. Define a weight function on total coloring as \begin{document} $ \phi(x) = f(x)+\sum\limits_{e\ni x}f(e)+\sum\limits_{y\in N(x)}f(y), $ \end{doc…
View article: Odd-Graceful Total Colorings for Constructing Graphic Lattice
Odd-Graceful Total Colorings for Constructing Graphic Lattice Open
The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture. A graphic lattice is generated by a graphic base and graphical operat…
View article: Mean Hitting Time for Random Walks on a Class of Sparse Networks
Mean Hitting Time for Random Walks on a Class of Sparse Networks Open
For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which…
View article: Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding
Exploring Relationship Between Traditional Lattices and Graph Lattices of Topological Coding Open
It is known that there are no polynomial quantum algorithms to solve some lattice difficult problems. Uncolored graphic lattice and colored graphic lattice are the products of multidisciplinary intersection inspired by lattice theory. A un…
View article: A note on 1-2-3 and 1-2 Conjectures for 3-regular graphs
A note on 1-2-3 and 1-2 Conjectures for 3-regular graphs Open
The 1-2-3 Conjecture, posed by Karoński, Łuczak and Thomason, asked whether every connected graph $G$ different from $K_2$ can be 3-edge-weighted so that every two adjacent vertices of $G$ get distinct sums of incident weights. The 1-2 Con…
View article: Recent Colorings And Labelings In Topological Coding
Recent Colorings And Labelings In Topological Coding Open
Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption syst…
View article: Matching-Type Image-Labelings of Trees
Matching-Type Image-Labelings of Trees Open
A variety of labelings on trees have emerged in order to attack the Graceful Tree Conjecture, but lack showing the connections between two labelings. In this paper, we propose two new labelings: vertex image-labeling and edge image-labelin…
View article: Mean First-Passage Time on Scale-Free Networks Based on Rectangle Operation
Mean First-Passage Time on Scale-Free Networks Based on Rectangle Operation Open
The mean first-passage time of random walks on a network has been extensively applied in the theory and practice of statistical physics, and its application effects depend on the behavior of first-passage time. Here, we firstly define a gr…
View article: Dense Networks With Mixture Degree Distribution
Dense Networks With Mixture Degree Distribution Open
Complex networks have become a powerful tool to describe the structure and evolution in a large quantity of real networks in the past few years, such as friendship networks, metabolic networks, protein–protein interaction networks, and sof…
View article: Arbitrary degree distribution networks with perturbations
Arbitrary degree distribution networks with perturbations Open
Complex networks have played an important role in the field of natural science and social science, attracting considerable attention of more and more scholars. Currently, scholars have proposed numbers of complex networks, in which some sh…