A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS

In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133).

Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

Analysis on the Changes of Research Hotspots in the Prevention and Treatment of COVID-19 by Traditional Chinese Medicine Based on Knowledge Graph

Objective: To grasp the changing trend of research hotspots of traditional Chinese medicine in the prevention and treatment of COVID-19, and to better play the role of traditional Chinese medicine in the prevention and treatment of COVID-19 and other diseases. Methods: The research literature from 2020 to 2022 was searched in the CNKI database, and CiteSpace software was used for visual analysis. Results: The papers on the prevention and treatment of COVID-19 by traditional Chinese medicine changed from cases, overviews, reports, and efficacy studies to more in-depth mechanism research, theoretical exploration, and social impact analysis, and finally formed a theory-clinical-society Influence-institutional change and other multi-dimensional achievement systems. Conclusion: Analyzing the changing trends of TCM hotspots in the prevention and treatment of COVID-19 can fully understand the important value of TCM, take the coordination of TCM and Western medicine as an important means to deal with public health security incidents, and promote the exploration of the potential efficacy of TCM, so as to enhance the role of TCM in Applications in social stability, emergency security, clinical practice, etc.

On an Invariant of Tournament Digraphs

To date, it is unknown whether it is possible to construct a complete graph invariant in polynomial time, so fast algorithms for checking non-isomorphism are important, including heuristic algorithms, and for successful implementations of such heuristics, both the tasks of some modification of previously described graph invariants and the description of new invariants remain relevant. Many of the described invariants make it possible to distinguish a larger number of graphs in the real time of a computer program. In this paper, we propose an invariant for a special kind of directed graphs, namely, for tournaments. The last ones, from our point of view, are interesting because when fixing the order of vertices, the number of different tournaments is exactly equal to the number of undirected graphs, also with fixing the order of vertices. In the invariant we are considering, all possible tournaments consisting of a subset of vertices of a given digraph with the same set of arcs are iterated over. For such subset tournaments, the places are calculated in the usual way, which are summed up to obtain the final values of the points of the vertices;these points form the proposed invariant. As we expected, calculations of the new invariant showed that it does not coincide with the most natural invariant for tournaments, in which the number of points is calculated for each participant. So far, we have conducted a small number of computational experiments, and the minimum value of the pair correlation between the sequences representing these two invariants that we found is for dimension 15.

Weak External Bisection of Some Graphs

Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V1 ∪ V2 and V1 ∩ V2 = ∅. If a bipartition satisfies ∥V1∣ - ∣V2∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V1, V2) such that ∀v ∈ V1, at least half minuses one of the neighbors of v are in the V2;∀v ∈ V2, at least half minuses one of the neighbors of v are in the V1. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.

Carbon Emission Factors Prediction of Power Grid by Using Graph Attention Network

Advanced carbon emission factors of a power grid can provide users with effective carbon reduction advice,which is of immense importance in mobilizing the entire society to reduce carbon emissions.The method of calculating node carbon emission factors based on the carbon emissions flow theory requires real-time parameters of a power grid.Therefore,it cannot provide carbon factor information beforehand.To address this issue,a prediction model based on the graph attention network is proposed.The model uses a graph structure that is suitable for the topology of the power grid and designs a supervised network using the loads of the grid nodes and the corresponding carbon factor data.The network extracts features and transmits information more suitable for the power system and can flexibly adjust the equivalent topology,thereby increasing the diversity of the structure.Its input and output data are simple,without the power grid parameters.We demonstrated its effect by testing IEEE-39 bus and IEEE-118 bus systems with average error rates of 2.46%and 2.51%.

On the (Δ + 2)-Total-Colorability of Planar Graphs with 7-Cycles Containing at Most Two Chords

The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords.

基于GChebyNet-GRU的超宽带高精度室内定位方法

超宽带高精度定位作为5G重大应用场景的关键技术,定位准确度极易受到室内复杂环境的干扰。为提高室内复杂环境下超宽带三维空间定位精度,提出了一种结合切比雪夫图卷积以及门控循环单元网络的定位模型。通过切比雪夫图卷积网络聚合静态的图结构和动态节点信息,结合门控循环网络捕捉节点间的依赖关系,进而精准预测靶点空间位置。实验结果表明,该模型相比于门控循环网络定位模型,无信号干扰情况下,X、Y、Z方向上的精度分别提高28.29%、41.48%、52.99%;有信号干扰情况下,精度分别提高34.95%、41.70%、36.43%,有效提高了基站处于信号干扰时室内定位的精度,更适合动态复杂的室内环境。

基于改进YOLOv7和ByteTrack的煤矿关键岗位人员不安全行为识别

应用人工智能技术对矿井提升机司机等煤矿关键岗位人员的行为进行实时识别,防止发生设备误操作等危险情况,对保障煤矿安全生产具有重要意义。针对基于图像特征的人员行为识别方法存在的抗背景干扰能力差与实时性不足问题,提出了一种基于改进YOLOv7和ByteTrack的煤矿关键岗位人员不安全行为识别方法。首先,基于MobileOne和C3对YOLOv7目标检测模型骨干与头部网络进行轻量化改进,提高模型推理速度;其次,融合ByteTrack跟踪算法,实现工作人员跟踪锁定,提高抗背景干扰能力;然后,采用MobileNetV2优化OpenPose的网络结构,提高对骨架特征的提取效率;最后,通过时空图卷积网络(ST−GCN)分析人体骨架关键点在时间序列上的空间结构和动态变化,实现对不安全行为的分析识别。实验结果表明:MobileOneC3−YOLO模型的精确率达93.7%,推理速度较YOLOv7模型提高了52%;融合ByteTrack的人员锁定模型锁定成功率达97.1%;改进OpenPose模型内存需求减少了170.3 MiB,在CPU与GPU上的推理速度分别提升了74.7%和54.9%;不安全行为识别模型对疲劳睡岗、离岗、侧身交谈和玩手机4种不安全行为的识别精确率达93.5%,推理速度达18.6帧/s。

基于改进GraphSAGE算法的浏览器指纹追踪

当前Web追踪领域主要使用浏览器指纹对用户进行追踪。针对浏览器指纹追踪技术存在指纹随时间动态变化、不易长期追踪等问题,提出一种关注节点和边缘特征的改进图采样聚合算法(An Improved Graph SAmple and AGgregatE with Both Node and Edge Features,NE-GraphSAGE)用于浏览器指纹追踪。首先以浏览器指纹为节点、指纹之间特征相似度为边构建图数据。其次对图神经网络中的GraphSAGE算法进行改进使其不仅能关注节点特征,而且能捕获边缘信息并对边缘分类,从而识别指纹。最后将NE-GraphSAGE算法与Eckersley算法、FPStalker算法和LSTM算法进行对比,验证NE-GraphSAGE算法的识别效果。实验结果表明,NE-GraphSAGE算法在准确率和追踪时长上均有不同程度的提升,最大追踪时长可达80天,相比其他3种算法性能更优,验证了NE-GraphSAGE算法对浏览器指纹长期追踪的能力。

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

Graph theory has a significant impact and is crucial in the structure of many real-life situations.To simulate uncertainty and ambiguity,many extensions of graph theoretical notions were created.Planar graphs play a vital role in modelling which has the property of non-crossing edges.Although crossing edges benefit,they have some drawbacks,which paved the way for the introduction of planar graphs.The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph.The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs.The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs,a conceptual blending of Pythagorean Neutro-sophic and Planar graphs.The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations.This paper investigates the Pythagorean Neutrosophic planar values,which form the edges of the Pythagorean neutrosophic graphs.The concept of Pythagorean Neutrosophic dual graphs,isomorphism,co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs.A decision-making algorithm was proposed with a numerical illustra-tion by using the Pythagorean Neutrosophic fuzzy graph.

Ordering of Unicyclic Graphs with Perfect Matchings by Minimal Matching Energies

In 2012, Gutman and Wagner proposed the concept of the matching energy of a graph and pointed out that its chemical applications can go back to the 1970s. The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let u and v be the non-isolated vertices of the graphs G and H with the same order, respectively. Let wi?be a non-isolated vertex of graph Gi?where i=1, 2, …, k. We use Gu(k)?(respectively, Hv(k)) to denote the graph which is the coalescence of G (respectively, H) and G1, G2,…, Gk?by identifying the vertices u (respectively, v) and w1, w2,…, wk. In this paper, we first present a new technique of directly comparing the matching energies of Gu(k)?and Hv(k), which can tackle some quasi-order incomparable problems. As the applications of the technique, then we can determine the unicyclic graphs with perfect matchings of order 2n with the first to the ninth smallest matching energies for all n≥211.

Topological Evaluation of Certain Computer Networks by Contraharmonic-Quadratic Indices

In various fields,different networks are used,most of the time not of a single kind;but rather a mix of at least two networks.These kinds of networks are called bridge networks which are utilized in interconnection networks of PC,portable networks,spine of internet,networks engaged with advanced mechanics,power generation interconnection,bio-informatics and substance intensify structures.Any number that can be entirely calculated by a graph is called graph invariants.Countless mathematical graph invariants have been portrayed and utilized for connection investigation during the latest twenty years.Nevertheless,no trustworthy evaluation has been embraced to pick,how much these invariants are associated with a network graph or subatomic graph.In this paper,it will discuss three unmistakable varieties of bridge networks with an incredible capacity of assumption in the field of computer science,chemistry,physics,drug industry,informatics and arithmetic in setting with physical and manufactured developments and networks,since Contraharmonic-quadratic invariants(CQIs)are recently presented and have different figure qualities for different varieties of bridge graphs or networks.The study settled the geography of bridge graphs/networks of three novel sorts with two kinds of CQI and Quadratic-Contraharmonic Indices(QCIs).The deduced results can be used for the modeling of the above-mentioned networks.

On the Spectral Properties of Graphs with Rank 4

Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.

Estrada index of dynamic random graphs

The Estrada index of a graph G on n vertices is defined by EE(G)=∑^(n)_(i=1)^(eλ_(i)),whereλ_(1),λ_(2),···,λ_(n)are the adjacency eigenvalues of G.We define two general types of dynamic graphs evolving according to continuous-time Markov processes with their stationary distributions matching the Erd¨os-R´enyi random graph and the random graph with given expected degrees,respectively.We formulate some new estimates and upper and lower bounds for the Estrada indices of these dynamic graphs.

Singularity of Two Kinds of Quadcyclic Peacock Graphs

Let G be a graph. G is singular if and only if the adjacency matrix of graph G is singular. The adjacency matrix of graph G is singular if and only if there is at least one zero eigenvalue. The study of the singularity of graphs is of great significance for better characterizing the properties of graphs. The following definitions are given. There are 4 paths, the starting points of the four paths are bonded into one point, and the ending point of each path is bonded to a cycle respectively, so this graph is called a kind of quadcyclic peacock graph. And in this kind of quadcyclic peacock graph assuming the number of points on the four cycles is a1, a2, a3, a4, and the number of points on the four paths is s1, s2, s3, s4, respectively. This type of graph is denoted by γ (a1, a2, a3, a4, s1, s2, s3, s4), called γ graph. And let γ (a1, a2, a3, a4, 1, 1, 1, 1) = δ (a1, a2, a3, a4), this type four cycles peacock graph called δ graph. In this paper, we give the necessary and sufficient conditions for the singularity of γ graph and δ graph.

A Remark on the Characterization of Triangulated Graphs

In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.