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Resource Allocation in V2X Networks:A Double Deep Q-Network Approach with Graph Neural Networks
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作者 Zhengda Huan Jian Sun +3 位作者 Zeyu Chen Ziyi Zhang Xiao Sun Zenghui Xiao 《Computers, Materials & Continua》 2025年第9期5427-5443,共17页
With the advancement of Vehicle-to-Everything(V2X)technology,efficient resource allocation in dynamic vehicular networks has become a critical challenge for achieving optimal performance.Existing methods suffer from h... With the advancement of Vehicle-to-Everything(V2X)technology,efficient resource allocation in dynamic vehicular networks has become a critical challenge for achieving optimal performance.Existing methods suffer from high computational complexity and decision latency under high-density traffic and heterogeneous network conditions.To address these challenges,this study presents an innovative framework that combines Graph Neural Networks(GNNs)with a Double Deep Q-Network(DDQN),utilizing dynamic graph structures and reinforcement learning.An adaptive neighbor sampling mechanism is introduced to dynamically select the most relevant neighbors based on interference levels and network topology,thereby improving decision accuracy and efficiency.Meanwhile,the framework models communication links as nodes and interference relationships as edges,effectively capturing the direct impact of interference on resource allocation while reducing computational complexity and preserving critical interaction information.Employing an aggregation mechanism based on the Graph Attention Network(GAT),it dynamically adjusts the neighbor sampling scope and performs attention-weighted aggregation based on node importance,ensuring more efficient and adaptive resource management.This design ensures reliable Vehicle-to-Vehicle(V2V)communication while maintaining high Vehicle-to-Infrastructure(V2I)throughput.The framework retains the global feature learning capabilities of GNNs and supports distributed network deployment,allowing vehicles to extract low-dimensional graph embeddings from local observations for real-time resource decisions.Experimental results demonstrate that the proposed method significantly reduces computational overhead,mitigates latency,and improves resource utilization efficiency in vehicular networks under complex traffic scenarios.This research not only provides a novel solution to resource allocation challenges in V2X networks but also advances the application of DDQN in intelligent transportation systems,offering substantial theoretical significance and practical value. 展开更多
关键词 Resource allocation V2X double deep Q-network graph neural network
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基于改进Graph2Seq的实体融合摘要生成模型
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作者 陶源 钱惠敏 《计算机与现代化》 2025年第6期1-8,共8页
针对现有摘要生成模型占用计算资源大和对关键命名实体信息关注不足的问题,基于Graph2Seq模型提出一种融合实体和稀疏注意力的文摘生成模型(ESG2S)。首先,将原始文本构建为句法依存图,并进行实体节点增强,得到图数据;其次,将构建好的图... 针对现有摘要生成模型占用计算资源大和对关键命名实体信息关注不足的问题,基于Graph2Seq模型提出一种融合实体和稀疏注意力的文摘生成模型(ESG2S)。首先,将原始文本构建为句法依存图,并进行实体节点增强,得到图数据;其次,将构建好的图数据送入编码器,进行文本结构的学习;最后,将编码后的图数据送入融合了对称散度增强稀疏注意力的LSTM解码器,生成多条摘要。在CNN/DM数据集上进行实验,结果表明本文模型效果优于近年的一些主流方法,并在实体信息保留上取得了成效,生成的摘要可读性和信息全面性更佳。 展开更多
关键词 关键词摘要生成 graph2Seq 命名实体 稀疏注意力
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Graph neural network-driven prediction of high-performance CO_(2)reduction catalysts based on Cu-based high-entropy alloys
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作者 Zihao Jiao Chengyi Zhang +2 位作者 Ya Liu Liejin Guo Ziyun Wang 《Chinese Journal of Catalysis》 2025年第4期197-207,共11页
High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface compl... High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface complexity and tendency for elemental segregation,which results in discrepancies between bulk and surface compositions,pose challenges for direct investigation via density functional theory.To address this,Monte Carlo simulations combined with molecular dynamics were employed to model surface segregation across a broad range of elements,including Cu,Ag,Au,Pt,Pd,and Al.The analysis revealed a trend in surface segregation propensity following the order Ag>Au>Al>Cu>Pd>Pt.To capture the correlation between surface site characteristics and the free energy of multi-dentate CO_(2)reduction intermediates,a graph neural network was designed,where adsorbates were transformed into pseudo-atoms at their centers of mass.This model achieved mean absolute errors of 0.08–0.15 eV for the free energies of C_(2)intermediates,enabling precise site activity quantification.Results indicated that increasing the concentration of Cu,Ag,and Al significantly boosts activity for CO and C_(2)formation,whereas Au,Pd,and Pt exhibit negative effects.By screening stable composition space,promising HEA bulk compositions for CO,HCOOH,and C_(2)products were predicted,offering superior catalytic activity compared to pure Cu catalysts. 展开更多
关键词 Density functional theory Machine learning CO_(2)reduction High entropy alloys graph neural network
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On Product-Cordial Index Sets and Friendly Index Sets of 2-Regular Graphs and Generalized Wheels 被引量:2
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作者 Harris KWONG Sin Min LEE Ho Kuen NG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第4期661-674,共14页
A vertex labeling f : V →Z2 of a simple graph G = (V, E) induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and d... A vertex labeling f : V →Z2 of a simple graph G = (V, E) induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs. 展开更多
关键词 Friendly index set product cordial index set 2-regular graphs generalized wheels
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不含3-,4-,7-圈平面图的2-距离染色
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作者 卜月华 包智敏 朱洪国 《浙江师范大学学报(自然科学版)》 2025年第2期133-141,共9页
通过分析极小反例平面图的结构性质,并运用权转移技巧,研究了不含3-,4-,7-圈平面图的2-距离色数.证明了Δ≥24且无3-,4-,7-圈的平面图G,有χ_(2)(G)≤Δ+3.该研究结果推广了此类平面图的2-距离染色的已知结果.
关键词 平面图 2-距离染色 权转移
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Graph neural network-based scheduling for multi-UAV-enabled communications in D2D networks 被引量:1
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作者 Pei Li Lingyi Wang +3 位作者 Wei Wu Fuhui Zhou Baoyun Wang Qihui Wu 《Digital Communications and Networks》 SCIE CSCD 2024年第1期45-52,共8页
In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission... In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means. 展开更多
关键词 Unmanned aerial vehicle D2 Dcommunication graph neural network Power control Position planning
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仙人掌图的D(2)-点可区别全染色
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作者 高杨 汪银芳 +1 位作者 文飞 李沐春 《高校应用数学学报(A辑)》 北大核心 2025年第2期243-252,共10页
图G的k-D(2)-点可区别全染色是G的一个正常k-全染色f满足对■u,v∈V(G),当dG(u,v)≤2时都有C_(f)(u)≠C_(f)(v),其中C_(f)(u)={f(u)}∪{f(uv)|uv∈E(G)}.将所用颜色数的最小值k称为图G的D(2)-点可区别全色数,简记为χ_(2vt)(G).应用数... 图G的k-D(2)-点可区别全染色是G的一个正常k-全染色f满足对■u,v∈V(G),当dG(u,v)≤2时都有C_(f)(u)≠C_(f)(v),其中C_(f)(u)={f(u)}∪{f(uv)|uv∈E(G)}.将所用颜色数的最小值k称为图G的D(2)-点可区别全色数,简记为χ_(2vt)(G).应用数学归纳法结合Hall定理考虑了仙人掌图G_(T)的D(2)-点可区别全染色,得到了χ_(2vt)(GT)≤Δ+3. 展开更多
关键词 仙人掌图 Hall定理 D(2)-点可区别全染色 D(2)-点可区别全色数
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圈图与简单图的冠图的D(2)-点和可区别边染色的界
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作者 何静 强会英 《吉林大学学报(理学版)》 北大核心 2025年第2期375-381,共7页
利用组合零点定理、构造染色法和数学归纳法,研究圈图与简单图的冠图的D(2)-点和可区别边染色问题,得到了圈图与简单图的冠图的D(2)-点和可区别边色数的界为Δ(G)+1,进而推出路图与简单图的冠图的界为Δ(G)+1.
关键词 圈图 简单图 冠图 D(2)-点和可区别边染色 D(2)-点和可区别边色数
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2-Factors with a Few Components in Balanced Bipartite Graphs
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作者 Huanxin Pei 《Engineering(科研)》 2024年第11期361-370,共10页
In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k compon... In this paper, a sufficient condition for a balanced bipartite graph to contain a 2-factor F is given. We show that every balanced bipartite graph of order 2n (n≥6)and e(G)>n2−2n+4contains a 2-factor with k components, 2d1-cycle, ⋯, 2dk-cycle, if one of the following is satisfied: (1) k=2, δ(G)≥2and d1−2≥d2≥2;(2) k=3, δ(G)≥d3+2and d1−2≥d2≥d3≥4. In particular, this extends one result of Moon and Moser in 1963 under condition (1). 展开更多
关键词 2-Factor Bipartite graph Degree Condition
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基于MASTGCN的AIS信息船舶SO_(2)排放预测模型
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作者 姚丹阳 岳明齐 +2 位作者 张珣 武芳 程诗茗 《交通信息与安全》 北大核心 2025年第2期65-73,共9页
船舶排放的二氧化硫(SO_(2))是导致大气污染和海洋酸化的主要因素之一,其时空分异性显著且不均,当前船舶污染物预测模型在时空依赖性建模方面存在局限性,难以有效捕捉船舶SO_(2)排放中的复杂时空关联特征。针对该问题,基于船舶自动识别... 船舶排放的二氧化硫(SO_(2))是导致大气污染和海洋酸化的主要因素之一,其时空分异性显著且不均,当前船舶污染物预测模型在时空依赖性建模方面存在局限性,难以有效捕捉船舶SO_(2)排放中的复杂时空关联特征。针对该问题,基于船舶自动识别系统(automatic identification system,AIS)数据及中国船舶基础信息数据,采用动力学方法结合排放因子量化船舶航行过程中的SO_(2)排放量,为后续预测提供了数据支持。在预测模型构建方面,研究了融合多头自注意力机制的时空图卷积网络(multi-head attention spatial-temporal graph convolutional network,MASTGCN)预测模型。该模型以时空图卷积网络(spatial-temporal graph convolutional network,STGCN)为基础架构,在空间和时间维度中引入多头自注意力机制,通过动态权重分配强化对不同区域间空间关联性以及不同时段间时间关联性的建模能力,实现对船舶SO_(2)排放的时空预测。实验结果表明,在注意力头数为5时,模型的平均绝对误差(mean absolute error,MAE)、均方误差(mean squared error,MSE)、均方根误差(root mean squared error,RMSE)以及浮点运算数(floating point operations,FLOPs)分别为0.057 5、0.120 6、0.347 3、3 030 M,模型准确度和计算复杂度的综合性能优于其他头数配置及STGCN模型。相较于STGCN模型,MAE、MSE、RMSE和FLOPs指标分别提高了27.6%、6.0%和1.3%。研究结果表明,多头注意力机制可以通过动态权重分配有效捕获船舶SO_(2)排放的空间特征,5个注意力头的MASTGCN模型在预测精度上表现优秀,同时在计算复杂度方面保持相对合理。 展开更多
关键词 绿色航运 AIS数据 船舶SO_(2)排放预测 时空图卷积模型 多头注意力机制
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树高不为零的三圈图的D(2)-点和可区别全染色
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作者 白羽 强会英 何静 《吉林大学学报(理学版)》 北大核心 2025年第4期1075-1082,共8页
用分析法、反证法和组合零点定理,研究树高不为零的三圈图的D(2)-点和可区别全染色问题,得到了该类图的D(2)-点和可区别全色数的一个上界为Δ(G)+3.
关键词 三圈图 D(2)-点和可区别全染色 D(2)-点和可区别全色数
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Ontology Matching Method Based on Gated Graph Attention Model
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作者 Mei Chen Yunsheng Xu +1 位作者 Nan Wu Ying Pan 《Computers, Materials & Continua》 2025年第3期5307-5324,共18页
With the development of the Semantic Web,the number of ontologies grows exponentially and the semantic relationships between ontologies become more and more complex,understanding the true semantics of specific terms o... With the development of the Semantic Web,the number of ontologies grows exponentially and the semantic relationships between ontologies become more and more complex,understanding the true semantics of specific terms or concepts in an ontology is crucial for the matching task.At present,the main challenges facing ontology matching tasks based on representation learning methods are how to improve the embedding quality of ontology knowledge and how to integrate multiple features of ontology efficiently.Therefore,we propose an Ontology Matching Method Based on the Gated Graph Attention Model(OM-GGAT).Firstly,the semantic knowledge related to concepts in the ontology is encoded into vectors using the OWL2Vec^(*)method,and the relevant path information from the root node to the concept is embedded to understand better the true meaning of the concept itself and the relationship between concepts.Secondly,the ontology is transformed into the corresponding graph structure according to the semantic relation.Then,when extracting the features of the ontology graph nodes,different attention weights are assigned to each adjacent node of the central concept with the help of the attention mechanism idea.Finally,gated networks are designed to further fuse semantic and structural embedding representations efficiently.To verify the effectiveness of the proposed method,comparative experiments on matching tasks were carried out on public datasets.The results show that the OM-GGAT model can effectively improve the efficiency of ontology matching. 展开更多
关键词 Ontology matching representation learning OWL2Vec*method graph attention model
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Detect the disrupted brain structural connectivity in type 2 diabetes mellitus patients without cognitive impairment
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作者 Yi-Fan Li Yue Wei +8 位作者 Ming-Rui Li Zhi-Zhong Sun Wei-Yan Xie Qian-Fan Li Chen-Hui Xie Jing-Yi Xiang XinTan Shi-Jun Qiu Yi Liang 《World Journal of Diabetes》 2025年第7期91-101,共11页
BACKGROUND Cognitive decline in type 2 diabetes mellitus(T2DM)occurs years before the onset of clinical symptoms.Early detection of this incipient cognitive decline stage,which is T2DM without mild cognitive impairmen... BACKGROUND Cognitive decline in type 2 diabetes mellitus(T2DM)occurs years before the onset of clinical symptoms.Early detection of this incipient cognitive decline stage,which is T2DM without mild cognitive impairment,is critical for clinical intervention,yet it remains elusive and challenging to identify.AIM To identify structural changes in the brains of T2DM patients without cognitive impairment to gain insights into the early-stage cognitive decline.METHODS Using diffusion tensor imaging(DTI),we constructed structural brain networks in 47 T2DM patients and 47 age-/sex-matched healthy controls.Machine learning models incorporating connectivity features were developed to classify T2DM brains and predict disease duration.RESULTS T2DM patients exhibited reduced global/local efficiency and small-worldness,alongside weakened connectivity in cortical regions but enhanced subcortical-frontal connections,suggesting compensatory mechanisms.A classification model leveraging 18 connectivity features achieved 92.5%accuracy in distinguishing T2DM brains.Structural connectivity patterns further predicted disease onset with an error of±1.9 years.CONCLUSION Our findings reveal early-stage brain network reorganization in T2DM,highlighting subcortical-frontal connectivity as a compensatory biomarker.The high-accuracy models demonstrate the potential of DTI-based biomarkers for preclinical cognitive decline detection. 展开更多
关键词 Type 2 diabetes mellitus White matter Diffusion tensor imaging Cognitive impairment graph theoretical analysis
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TCMLCM:an intelligent question-answering model for traditional Chinese medicine lung cancer based on the KG2TRAG method
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作者 Chunfang ZHOU Qingyue GONG +2 位作者 Wendong ZHAN Jinyang ZHU Huidan LUAN 《Digital Chinese Medicine》 2025年第1期36-45,共10页
Objective To improve the accuracy and professionalism of question-answering(QA)model in traditional Chinese medicine(TCM)lung cancer by integrating large language models with structured knowledge graphs using the know... Objective To improve the accuracy and professionalism of question-answering(QA)model in traditional Chinese medicine(TCM)lung cancer by integrating large language models with structured knowledge graphs using the knowledge graph(KG)to text-enhanced retrievalaugmented generation(KG2TRAG)method.Methods The TCM lung cancer model(TCMLCM)was constructed by fine-tuning Chat-GLM2-6B on the specialized datasets Tianchi TCM,HuangDi,and ShenNong-TCM-Dataset,as well as a TCM lung cancer KG.The KG2TRAG method was applied to enhance the knowledge retrieval,which can convert KG triples into natural language text via ChatGPT-aided linearization,leveraging large language models(LLMs)for context-aware reasoning.For a comprehensive comparison,MedicalGPT,HuatuoGPT,and BenTsao were selected as the baseline models.Performance was evaluated using bilingual evaluation understudy(BLEU),recall-oriented understudy for gisting evaluation(ROUGE),accuracy,and the domain-specific TCM-LCEval metrics,with validation from TCM oncology experts assessing answer accuracy,professionalism,and usability.Results The TCMLCM model achieved the optimal performance across all metrics,including a BLEU score of 32.15%,ROUGE-L of 59.08%,and an accuracy rate of 79.68%.Notably,in the TCM-LCEval assessment specific to the field of TCM,its performance was 3%−12%higher than that of the baseline model.Expert evaluations highlighted superior performance in accuracy and professionalism.Conclusion TCMLCM can provide an innovative solution for TCM lung cancer QA,demonstrating the feasibility of integrating structured KGs with LLMs.This work advances intelligent TCM healthcare tools and lays a foundation for future AI-driven applications in traditional medicine. 展开更多
关键词 Traditional Chinese medicine(TCM) Lung cancer Question-answering Large language model Fine-tuning Knowledge graph KG2TRAG method
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最大度为4的平面图的2-距离染色
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作者 卜月华 朱旭波 朱俊蕾 《数学进展》 CSCD 北大核心 2024年第2期281-291,共11页
2-距离染色是使得距离至多为2的顶点染不同色的一种顶点染色.1977年,Wegner猜想9种颜色可以使最大度为4的平面图有一个2-距离染色.本文证明了最大度为4的平面图用13种颜色可以使之有一个2-距离染色,而对不含三角形且最大度为4的平面图... 2-距离染色是使得距离至多为2的顶点染不同色的一种顶点染色.1977年,Wegner猜想9种颜色可以使最大度为4的平面图有一个2-距离染色.本文证明了最大度为4的平面图用13种颜色可以使之有一个2-距离染色,而对不含三角形且最大度为4的平面图用11种颜色就可以了. 展开更多
关键词 平面图 2-距离染色 最大度 围长 Wegner猜想
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单圈图的D(2)-点和可区别全染色
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作者 强会英 刘欢 王洪申 《高校应用数学学报(A辑)》 北大核心 2024年第3期371-378,共8页
图G的D(2)-点和可区别全染色是指在图G的一个正常全染色φ下,G中任意两个距离不超过2的顶点u,v,其色集合中所有颜色数之和互不相同.使得G有一个k-D(2)-点和可区别全染色的最小整数k,称为图G的D(2)-点和可区别全色数.文中应用组合零点定... 图G的D(2)-点和可区别全染色是指在图G的一个正常全染色φ下,G中任意两个距离不超过2的顶点u,v,其色集合中所有颜色数之和互不相同.使得G有一个k-D(2)-点和可区别全染色的最小整数k,称为图G的D(2)-点和可区别全色数.文中应用组合零点定理和权转移方法刻画了单圈图的D(2)-点和可区别全染色,并得到其D(2)-点和可区别全色数. 展开更多
关键词 单圈图 全染色 D(2)-点和可区别全染色 权转移方法
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The Cordiality on the Union of 3-regular Connected Graph and Cycle 被引量:3
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作者 XIE Yan-tao CHE Ying-tao LIU Zhi-shan 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期244-248,共5页
Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph... Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm. 展开更多
关键词 3-regular graph Cordial graph union graph
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A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH 被引量:2
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作者 李德明 刘彦佩 《Acta Mathematica Scientia》 SCIE CSCD 1999年第4期375-381,共7页
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert... A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided. 展开更多
关键词 maximum genus nonseparating independent number feedback vertex set 3-regular graph adjacency matching
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2-Walk Linear Graphs with Small Number of Cycles 被引量:1
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作者 FAN Qiong QI Huan 《Wuhan University Journal of Natural Sciences》 CAS 2010年第5期375-379,共5页
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk(a,b)-linear graph must obey.Using these conditions and some basic the... A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk(a,b)-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs. 展开更多
关键词 2-walk linear graphs unicyclic graphs bicyclic graphs tricyclic graphs
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On L(1, 2)-Edge-Labelings of Some Special Classes of Graphs 被引量:2
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作者 Dan HE Wensong LIN 《Journal of Mathematical Research with Applications》 CSCD 2014年第4期403-413,共11页
For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which ... For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L(j, k)-edge-labeling admitted by G.In this article, we study the L(1, 2)-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ?-regular trees and wheels. 展开更多
关键词 L(j k)-edge-labeling line graph path cycle complete graph complete multipartite graph infinite -regular tree wheel
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