The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar ...The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this note,we completely characterize the semipotent rings whose unit graphs are planar.As a consequence,we list all semilocal rings with planar unit graphs.展开更多
Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.I...Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.展开更多
This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, mod...This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).展开更多
The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless n...The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless networks.Investigation of some properties of independent set(IS)in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms.Several constant factor approximation algorithms are presented for the CDS problem in UDGs.Simulation results show that the proposed algorithms perform better than some known ones.展开更多
In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying...Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying graph of(G,Φ),the circle group T and a gain functionΦ:→E→T such that φ(vivj)=φ(vjvi) for any adjacent vertices vi and vj.Let i+(G,φ)(resp.,i+(G))be the positive inertia index of(G,φ)(resp.,G).In this paper,we prove that-c(G)≤i+(G,φ)-i+(G)≤c(G),where c(G)is the cyclomatic number of G,and characterize all the corresponding extremal graphs.展开更多
钻井顶部驱动装置结构复杂、故障类型多样,现有的故障树分析法和专家系统难以有效应对复杂多变的现场情况。为此,利用知识图谱在结构化与非结构化信息融合、故障模式关联分析以及先验知识传递方面的优势,提出了一种基于知识图谱的钻井...钻井顶部驱动装置结构复杂、故障类型多样,现有的故障树分析法和专家系统难以有效应对复杂多变的现场情况。为此,利用知识图谱在结构化与非结构化信息融合、故障模式关联分析以及先验知识传递方面的优势,提出了一种基于知识图谱的钻井顶部驱动装置故障诊断方法,利用以Transformer为基础的双向编码器模型(Bidirectional Encoder Representations from Transformers,BERT)构建了混合神经网络模型BERT-BiLSTM-CRF与BERT-BiLSTM-Attention,分别实现了顶驱故障文本数据的命名实体识别和关系抽取,并通过相似度计算,实现了故障知识的有效融合和智能问答,最终构建了顶部驱动装置故障诊断方法。研究结果表明:①在故障实体识别任务上,BERT-BiLSTM-CRF模型的精确度达到95.49%,能够有效识别故障文本中的信息实体;②在故障关系抽取上,BERT-BiLSTM-Attention模型的精确度达到93.61%,实现了知识图谱关系边的正确建立;③开发的问答系统实现了知识图谱的智能应用,其在多个不同类型问题上的回答准确率超过了90%,能够满足现场使用需求。结论认为,基于知识图谱的故障诊断方法能够有效利用顶部驱动装置的先验知识,实现故障的快速定位与智能诊断,具备良好的应用前景。展开更多
基金supported by the National Natural Science Foundation of China(11661013,11661014,11961050)Guangxi Natural Science Foundation(2016GXNSFCA380014,2016GXNSFDA380017).
文摘The unit graph of a ring is the simple graph whose vertices are the elements of the ring and where two distinct vertices are adjacent if and only if their sum is a unit of the ring.A simple graph is said to be planar if it can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this note,we completely characterize the semipotent rings whose unit graphs are planar.As a consequence,we list all semilocal rings with planar unit graphs.
基金supported in part by a grant from Science and Engineering Research Board,India(Ref.MTR/2017/000830)supported by the National Natural Science Foundation of China(Ref.11961050)the Guangxi Natural Sciences Foundation(Ref.2021GXNSFAA220043).
文摘Let R be a ring with non-zero identity.The unit graph of R,denoted by G(R),is an undirected graph with all the elements of R as vertices and where distinct vertices x,y are adjacent if and only if x+y is a unit of R.In this paper,we investigate the Wiener index and hyper-Wiener index of G(R)and explicitly determine their values.
文摘This paper shows that, for every unit interval graph, there is a labelling which is simultaneously optimal for the following seven graph labelling problems: bandwidth, cyclic bandwidth, profile, fill-in, cutwidth, modified cutwidth, and bandwidth sum(linear arrangement).
基金supported by the National Natural Science Foundation of China under Grant No 60473090the National"11th Five-Year-Supporting-Plan"of China under Grant No 2006BAH02A0407
文摘The connected dominating set(CDS)problem,which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs(UDGs).This paper focuses on the CDS problem in wireless networks.Investigation of some properties of independent set(IS)in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms.Several constant factor approximation algorithms are presented for the CDS problem in UDGs.Simulation results show that the proposed algorithms perform better than some known ones.
基金Supported by the National Natural Science Foundation of China(Grant No.11771176)。
文摘In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
基金Supported by the National Natural Science Foundation of China(Grant No.11971474)the Natural Science Foundation of Shandong Province(Grant No.ZR2019BA016)。
文摘Let T be the subgroup of the multiplicative group C^(×)consisting of all complex numbers z with|z|=1.A T-gain graph is a tripleΦ=(G,T,φ)(or short for(G,φ))consisting of a simple graph G=(V,E),as the underlying graph of(G,Φ),the circle group T and a gain functionΦ:→E→T such that φ(vivj)=φ(vjvi) for any adjacent vertices vi and vj.Let i+(G,φ)(resp.,i+(G))be the positive inertia index of(G,φ)(resp.,G).In this paper,we prove that-c(G)≤i+(G,φ)-i+(G)≤c(G),where c(G)is the cyclomatic number of G,and characterize all the corresponding extremal graphs.
文摘钻井顶部驱动装置结构复杂、故障类型多样,现有的故障树分析法和专家系统难以有效应对复杂多变的现场情况。为此,利用知识图谱在结构化与非结构化信息融合、故障模式关联分析以及先验知识传递方面的优势,提出了一种基于知识图谱的钻井顶部驱动装置故障诊断方法,利用以Transformer为基础的双向编码器模型(Bidirectional Encoder Representations from Transformers,BERT)构建了混合神经网络模型BERT-BiLSTM-CRF与BERT-BiLSTM-Attention,分别实现了顶驱故障文本数据的命名实体识别和关系抽取,并通过相似度计算,实现了故障知识的有效融合和智能问答,最终构建了顶部驱动装置故障诊断方法。研究结果表明:①在故障实体识别任务上,BERT-BiLSTM-CRF模型的精确度达到95.49%,能够有效识别故障文本中的信息实体;②在故障关系抽取上,BERT-BiLSTM-Attention模型的精确度达到93.61%,实现了知识图谱关系边的正确建立;③开发的问答系统实现了知识图谱的智能应用,其在多个不同类型问题上的回答准确率超过了90%,能够满足现场使用需求。结论认为,基于知识图谱的故障诊断方法能够有效利用顶部驱动装置的先验知识,实现故障的快速定位与智能诊断,具备良好的应用前景。
