The undirected power graph <i>P</i>(<i>Z<sub>n</sub></i>) of a finite group <i>Z<sub>n</sub></i> is the graph with vertex set G and two distinct vertices u a...The undirected power graph <i>P</i>(<i>Z<sub>n</sub></i>) of a finite group <i>Z<sub>n</sub></i> is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if <i>u</i> ≠ <i>v</i> and <img src="Edit_3b1df203-9ff2-4c13-93d1-4bba568eae54.png" width="40" height="20" alt="" /> or <img src="Edit_094c8f88-deb6-4f41-825a-ba91c0306ae8.png" width="40" height="20" alt="" />. The Wiener index <i>W</i>(<i>P</i>(<i>Z<sub>n</sub></i>)) of an undirected power graph <i>P</i>(<i>Z<sub>n</sub></i>) is defined to be sum <img src="Edit_348337df-b9c2-480d-9713-ec299a6fcd4e.png" width="110" height="25" alt="" /> of distances between all unordered pair of vertices in <i>P</i>(<i>Z<sub>n</sub></i>). Similarly, the edge-Wiener index <i>W<sub>e</sub></i>(<i>P</i>(<i>Z<sub>n</sub></i>)) of <i>P</i>(<i>Z<sub>n</sub></i>) is defined to be the sum <img src="Edit_e9b89765-f71e-4865-a0c5-c688710ff0c6.png" width="60" height="25" alt="" /> of distances between all unordered pairs of edges in <i>P</i>(<i>Z<sub>n</sub></i>). In this paper, we concentrate on the wiener index of a power graph <img src="Edit_dff0cd99-eb11-4123-a437-78cbbd8ebf96.png" width="40" height="20" alt="" />, <i>P</i>(<i>Z<sub>pq</sub></i>) and <i>P</i>(<i>Z<sub>p</sub></i>). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph <i>P</i>(<i>Z<sub>n</sub></i>), using <i>m,n</i> and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of <i>Z<sub>n</sub></i>.展开更多
It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G ...It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.展开更多
Let G be a finite group of order n. The strong power graph of G is the undirected graph whose vertex set is G and two distinct vertices x and y are adjacent if x^n1 = y^n2 for some positive integers n1,n2 < n. In t...Let G be a finite group of order n. The strong power graph of G is the undirected graph whose vertex set is G and two distinct vertices x and y are adjacent if x^n1 = y^n2 for some positive integers n1,n2 < n. In this paper, we give the characteristic polynomials of the distance and adjacency matrix of the strong power graph of G, and compute its distance and adjacency spectrum.展开更多
.The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-....The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-trivial.A number of important graph classes,including cographs,chordal graphs,split graphs,and threshold graphs,can be defined either structurally or in terms of forbidden induced subgraphs.In this paper,we characterize the finite groups whose intersection power graphs are cographs,split graphs,and threshold graphs.We also classify the finite nilpotent groups whose intersection power graphs are chordal.展开更多
The enhanced power graph Pe(G)of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x,y are adjacent if x,y∈(z)for some z∈G.We give an affirmative answer to the question ...The enhanced power graph Pe(G)of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x,y are adjacent if x,y∈(z)for some z∈G.We give an affirmative answer to the question posed by Cameron which asks whether the complement of the enhanced power graph P_(E)(G)of a non-cyclic group G,P_(E)(G),has only one connected component apart from isolated vertices.We classify all finite groups G for which P_(E)(G)is bipartite.We show that the graph P_(E)(G)is weakly perfect.Further,we study the subgraph P_(E)(G^(*))of P_(E)(G)induced by all the non-isolated vertices of P_(E)(G).We classify all finite groups G with the graph P_(E)(G^(*))being unicyclic and pentacyclic,and we prove the non-existence of finite groups G such that the graph P_(E)(G^(*))is bicyclic,tricyclic or tetracyclic.Finally,we characterize all finite groups G for which the graph P_(E)(G^(*))is outerplanar,planar,projective-planar and toroidal separately.展开更多
The reduced power graph of a group G,denoted by RP(G),is the graph whose vertex set is the set of all elements of G and two vertices u and u are adjacent in RP(G)if and only if(u)C(u)or(u)C(u).In this paper,we study t...The reduced power graph of a group G,denoted by RP(G),is the graph whose vertex set is the set of all elements of G and two vertices u and u are adjacent in RP(G)if and only if(u)C(u)or(u)C(u).In this paper,we study the adjacency spectrum of the reduced power graph of Z_(n),Z^(n)_(p2),Z_(p2) x Z_(p),dihedral group,quaternion group and semi-dihedral group.展开更多
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In t...The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.展开更多
With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have cho...With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.展开更多
In this paper we study the relationship between minimum rank of graph G and the minimum rank of graph for some families of special graph G, where is the jth power of graph G.
电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故...电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故障预测的准确性,影响了电力系统的可靠运行。针对这一问题,该文提出了一种创新的基于GraphSAGE(Graph Sample and Aggregate)算法的电力物联设备故障预测。该方法通过PowerGraph数据集,将电力物联设备故障场景细分为四类,利用GraphSAGE模型的特性,深入学习和分析节点特征与边特征,从而实现对物联设备故障的有效预测。实验结果表明,该方法准确率达到97.5%,相较于其它传统方法,准确率提高了0.39%~6.21%,同时GraphSAGE模型实现了快速训练。该方法为电力物联设备安全稳定运行提供重要决策支持,能够对动态和相互联系的复杂系统进行更精细的分析,并增强电力系统运营部门对潜在干扰的预见和应对能力。展开更多
Scheduled maintenance and condition-based online monitoring are among the focal points of recent research to enhance nuclear plant safety.One of the most effective ways to monitor plant conditions is by implementing a...Scheduled maintenance and condition-based online monitoring are among the focal points of recent research to enhance nuclear plant safety.One of the most effective ways to monitor plant conditions is by implementing a full-scope,plant-wide fault diagnostic system.However,most of the proposed diagnostic techniques are perceived as unreliable by operators because they lack an explanation module,their implementation is complex,and their decision/inference path is unclear.Graphical formalism has been considered for fault diagnosis because of its clear decision and inference modules,and its ability to display the complex causal relationships between plant variables and reveal the propagation path used for fault localization in complex systems.However,in a graphbased approach,decision-making is slow because of rule explosion.In this paper,we present an enhanced signed directed graph that utilizes qualitative trend evaluation and a granular computing algorithm to improve the decision speed and increase the resolution of the graphical method.We integrate the attribute reduction capability of granular computing with the causal/fault propagation reasoning capability of the signed directed graph and comprehensive rules in a decision table to diagnose faults in a nuclear power plant.Qualitative trend analysis is used to solve the problems of fault diagnostic threshold selection and signed directed graph node state determination.The similarity reasoning and detection ability of the granular computing algorithm ensure a compact decision table and improve the decision result.The performance of the proposed enhanced system was evaluated on selected faults of the Chinese Fuqing 2 nuclear reactor.The proposed method offers improved diagnostic speed and efficient data processing.In addition,the result shows a considerable reduction in false positives,indicating that the method provides a reliable diagnostic system to support further intervention by operators.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we cons...<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial.展开更多
In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and lin...In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and linear discriminant principle to resolve fast and exact analysis of faulty components and faulty sections, and finally accomplish fault diagnosis. The results of BFS and linear discriminant are identical. The main technical contributions and innovations in this paper include, introducing global information into electric power network, developing a novel topological analysis to fault diagnosis. Graph theory algorithms can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object. In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.展开更多
文摘The undirected power graph <i>P</i>(<i>Z<sub>n</sub></i>) of a finite group <i>Z<sub>n</sub></i> is the graph with vertex set G and two distinct vertices u and v are adjacent if and only if <i>u</i> ≠ <i>v</i> and <img src="Edit_3b1df203-9ff2-4c13-93d1-4bba568eae54.png" width="40" height="20" alt="" /> or <img src="Edit_094c8f88-deb6-4f41-825a-ba91c0306ae8.png" width="40" height="20" alt="" />. The Wiener index <i>W</i>(<i>P</i>(<i>Z<sub>n</sub></i>)) of an undirected power graph <i>P</i>(<i>Z<sub>n</sub></i>) is defined to be sum <img src="Edit_348337df-b9c2-480d-9713-ec299a6fcd4e.png" width="110" height="25" alt="" /> of distances between all unordered pair of vertices in <i>P</i>(<i>Z<sub>n</sub></i>). Similarly, the edge-Wiener index <i>W<sub>e</sub></i>(<i>P</i>(<i>Z<sub>n</sub></i>)) of <i>P</i>(<i>Z<sub>n</sub></i>) is defined to be the sum <img src="Edit_e9b89765-f71e-4865-a0c5-c688710ff0c6.png" width="60" height="25" alt="" /> of distances between all unordered pairs of edges in <i>P</i>(<i>Z<sub>n</sub></i>). In this paper, we concentrate on the wiener index of a power graph <img src="Edit_dff0cd99-eb11-4123-a437-78cbbd8ebf96.png" width="40" height="20" alt="" />, <i>P</i>(<i>Z<sub>pq</sub></i>) and <i>P</i>(<i>Z<sub>p</sub></i>). Firstly, we obtain new results on the wiener index and edge-wiener index of power graph <i>P</i>(<i>Z<sub>n</sub></i>), using <i>m,n</i> and Euler function. Also, we obtain an equivalence between the edge-wiener index and wiener index of a power graph of <i>Z<sub>n</sub></i>.
基金Project supported by NSFC(10371112)NSFHN (0411011200)SRF for ROCS,SEM
文摘It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.
基金Supported by the National Natural Science Foundation of China(Grant No.11801441)the Scientific Research Program Funded by Shaanxi Provincial Education Department(Program No.18JK0623)the Natural Science Foundation of Shaanxi Province(Grant No.2019JQ-056)
文摘Let G be a finite group of order n. The strong power graph of G is the undirected graph whose vertex set is G and two distinct vertices x and y are adjacent if x^n1 = y^n2 for some positive integers n1,n2 < n. In this paper, we give the characteristic polynomials of the distance and adjacency matrix of the strong power graph of G, and compute its distance and adjacency spectrum.
基金supported by the National Natural Science Foundation of China(Grant Nos.11801441,61976244)the Natural Science Basic Research Program of Shaanxi(Program No.2020JQ-761)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ024).
文摘.The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-trivial.A number of important graph classes,including cographs,chordal graphs,split graphs,and threshold graphs,can be defined either structurally or in terms of forbidden induced subgraphs.In this paper,we characterize the finite groups whose intersection power graphs are cographs,split graphs,and threshold graphs.We also classify the finite nilpotent groups whose intersection power graphs are chordal.
基金support of CSIR(09/719(0110)/2019-EMR-I),government of Indiasupport from SERB(Core Research Grant(CRG/2022/001142)),government of India.
文摘The enhanced power graph Pe(G)of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x,y are adjacent if x,y∈(z)for some z∈G.We give an affirmative answer to the question posed by Cameron which asks whether the complement of the enhanced power graph P_(E)(G)of a non-cyclic group G,P_(E)(G),has only one connected component apart from isolated vertices.We classify all finite groups G for which P_(E)(G)is bipartite.We show that the graph P_(E)(G)is weakly perfect.Further,we study the subgraph P_(E)(G^(*))of P_(E)(G)induced by all the non-isolated vertices of P_(E)(G).We classify all finite groups G with the graph P_(E)(G^(*))being unicyclic and pentacyclic,and we prove the non-existence of finite groups G such that the graph P_(E)(G^(*))is bicyclic,tricyclic or tetracyclic.Finally,we characterize all finite groups G for which the graph P_(E)(G^(*))is outerplanar,planar,projective-planar and toroidal separately.
文摘The reduced power graph of a group G,denoted by RP(G),is the graph whose vertex set is the set of all elements of G and two vertices u and u are adjacent in RP(G)if and only if(u)C(u)or(u)C(u).In this paper,we study the adjacency spectrum of the reduced power graph of Z_(n),Z^(n)_(p2),Z_(p2) x Z_(p),dihedral group,quaternion group and semi-dihedral group.
基金Project supporte（t by the National Natural Science Foundation of China （Grant No.10571117）, and the Youth Science Foundation of Shanghai Municipal Commission of Education （Grant No.01QN6262）
文摘The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.
基金supported by the State Grid Science and Technology Project (Title: Research on High Performance Analysis Technology of Power Grid GIS Topology Based on Graph Database, 5455HJ160005)
文摘With the development of information technology, the amount of power grid topology data has gradually increased. Therefore, accurate querying of this data has become particularly important. Several researchers have chosen different indexing methods in the filtering stage to obtain more optimized query results because currently there is no uniform and efficient indexing mechanism that achieves good query results. In the traditional algorithm, the hash table for index storage is prone to "collision" problems, which decrease the index construction efficiency. Aiming at the problem of quick index entry, based on the construction of frequent subgraph indexes, a method of serialized storage optimization based on multiple hash tables is proposed. This method mainly uses the exploration sequence to make the keywords evenly distributed; it avoids conflicts of the stored procedure and performs a quick search of the index. The proposed algorithm mainly adopts the "filterverify" mechanism; in the filtering stage, the index is first established offline, and then the frequent subgraphs are found using the "contains logic" rule to obtain the candidate set. Experimental results show that this method can reduce the time and scale of candidate set generation and improve query efficiency.
文摘In this paper we study the relationship between minimum rank of graph G and the minimum rank of graph for some families of special graph G, where is the jth power of graph G.
文摘电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故障预测的准确性,影响了电力系统的可靠运行。针对这一问题,该文提出了一种创新的基于GraphSAGE(Graph Sample and Aggregate)算法的电力物联设备故障预测。该方法通过PowerGraph数据集,将电力物联设备故障场景细分为四类,利用GraphSAGE模型的特性,深入学习和分析节点特征与边特征,从而实现对物联设备故障的有效预测。实验结果表明,该方法准确率达到97.5%,相较于其它传统方法,准确率提高了0.39%~6.21%,同时GraphSAGE模型实现了快速训练。该方法为电力物联设备安全稳定运行提供重要决策支持,能够对动态和相互联系的复杂系统进行更精细的分析,并增强电力系统运营部门对潜在干扰的预见和应对能力。
基金supported by the project of State Key Laboratory of Nuclear Power Safety Monitoring Technology and Equipment(No.KA2019.418)the Foundation of Science and Technology on Reactor System Design Technology Laboratory(HT-KFKT-14-2017003)+1 种基金the technical support project for Suzhou Nuclear Power Research Institute(SNPI)(No.029-GN-B-2018-C45-P.0.99-00003)the project of the Research Institute of Nuclear Power Operation(No.RIN180149-SCCG)
文摘Scheduled maintenance and condition-based online monitoring are among the focal points of recent research to enhance nuclear plant safety.One of the most effective ways to monitor plant conditions is by implementing a full-scope,plant-wide fault diagnostic system.However,most of the proposed diagnostic techniques are perceived as unreliable by operators because they lack an explanation module,their implementation is complex,and their decision/inference path is unclear.Graphical formalism has been considered for fault diagnosis because of its clear decision and inference modules,and its ability to display the complex causal relationships between plant variables and reveal the propagation path used for fault localization in complex systems.However,in a graphbased approach,decision-making is slow because of rule explosion.In this paper,we present an enhanced signed directed graph that utilizes qualitative trend evaluation and a granular computing algorithm to improve the decision speed and increase the resolution of the graphical method.We integrate the attribute reduction capability of granular computing with the causal/fault propagation reasoning capability of the signed directed graph and comprehensive rules in a decision table to diagnose faults in a nuclear power plant.Qualitative trend analysis is used to solve the problems of fault diagnostic threshold selection and signed directed graph node state determination.The similarity reasoning and detection ability of the granular computing algorithm ensure a compact decision table and improve the decision result.The performance of the proposed enhanced system was evaluated on selected faults of the Chinese Fuqing 2 nuclear reactor.The proposed method offers improved diagnostic speed and efficient data processing.In addition,the result shows a considerable reduction in false positives,indicating that the method provides a reliable diagnostic system to support further intervention by operators.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial.
文摘In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and linear discriminant principle to resolve fast and exact analysis of faulty components and faulty sections, and finally accomplish fault diagnosis. The results of BFS and linear discriminant are identical. The main technical contributions and innovations in this paper include, introducing global information into electric power network, developing a novel topological analysis to fault diagnosis. Graph theory algorithms can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object. In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.
