Recently, the primitive symmetric signed digraphs on $n$ vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively...Recently, the primitive symmetric signed digraphs on $n$ vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on n vertices with the base 2n-1 are characterized, and then the primitive symmetric signed digraphs on n vertices with the second maximum base 2n-1 are characterized.展开更多
Let S be a primitive non-powerful symmetric loop-free signed digraph on even n vertices with base 3 and minimum number of arcs. In [Lihua YOU, Yuhan WU. Primitive non- powerful symmetric loop-free signed digraphs with...Let S be a primitive non-powerful symmetric loop-free signed digraph on even n vertices with base 3 and minimum number of arcs. In [Lihua YOU, Yuhan WU. Primitive non- powerful symmetric loop-free signed digraphs with given base and minimum number of arcs. Linear Algebra Appl., 2011, 434（5）, 1215-1227], authors conjectured that D is the underlying digraph of S with exp（D）= 3 if and only if D is isomorphic to EDn,3,3, where EDn,3,3 = （V, A） is a digraph with V = {1, 2,..., n}, A = {（1, i）, （i, 1） [ 3 〈： i 〈 n} U {（2i - 1, 2i）, （2i, 2i - 1） [ 2 〈 〈 2} U {（2, 3）, （3, 2）, （2, 4）, （4, 2）}）. In this paper, we show the conjecture is true and completely characterize the underlying digraphs which have base 3 and the minimum number of arcs.展开更多
Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in ...Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in SDG generated from chemical process. From the point of the inherent operability, the worst unsafe factor is the SDG having positive loops that means any disturbance occurring within the loop will propagate through the nodes one by one and are amplified gradually, so the system may lose control, which may lead to an accident. So finding the positive loops in a SDG and treating these unsafe factors in a proper manner can improve the inherent safety of a chemical process. This article proposed a method that can detect the above-mentioned unsafe factors in the proc- ess conceptual design stage automatically through the analysis of the SDG generated from the chemical process. A case study is illustrated to show the working of the algorithm, and then a complicated case from industry is studied to depict the effectiveness of the proposed algorithm.展开更多
In this paper, we study the bases and base sets of primitive symmetric loop-free （generalized） signed digraphs on n vertices. We obtain sharp upper bounds of the bases, and show that the base sets of the classes of ...In this paper, we study the bases and base sets of primitive symmetric loop-free （generalized） signed digraphs on n vertices. We obtain sharp upper bounds of the bases, and show that the base sets of the classes of such digraphs are （2, 3,..., 2n - 1}. We also give a new proof of an important result obtained by Cheng and Liu.展开更多
Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a majo...Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.展开更多
A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which...A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.展开更多
The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to ad...The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to address this issue.However,there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures.To support developers,researchers,and practitioners in this field,we introduce a Python library named SNSAlib(Signed Network Structure Analysis),specifically designed to meet these analytical requirements.This library encompasses empirical signed network datasets,signed null model algorithms,signed statistics algorithms,and evaluation indicators.The primary objective of SNSAlib is to facilitate the systematic analysis of micro-and meso-structure features within signed networks,including node popularity,clustering,assortativity,embeddedness,and community structure by employing more accurate signed null models.Ultimately,it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.展开更多
This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It ...The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.展开更多
A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for ...A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.展开更多
Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such ...Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.展开更多
A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）...A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1090106111071088)+1 种基金the Zhujiang Technology New Star Foundation of Guangzhou(Grant No.2011J2200090)Program on International Cooperation and Innovation of Guangdong Province Education Department(Grant No.2012gjhz0007)
文摘Recently, the primitive symmetric signed digraphs on $n$ vertices with the maximum base 2n and the primitive symmetric loop-free signed digraphs on n vertices with the maximum base 2n-1 are characterized, respectively. In this paper, the primitive symmetric signed digraphs with loops on n vertices with the base 2n-1 are characterized, and then the primitive symmetric signed digraphs on n vertices with the second maximum base 2n-1 are characterized.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1090106111071088)+1 种基金Programon International Cooperation and Innovation,Department of Education,Guangdong Province(Grant No.2012gjhz0007)the Zhujiang Technology New Star Foundation of Guangzhou City(Grant No.2011J2200090)
文摘Let S be a primitive non-powerful symmetric loop-free signed digraph on even n vertices with base 3 and minimum number of arcs. In [Lihua YOU, Yuhan WU. Primitive non- powerful symmetric loop-free signed digraphs with given base and minimum number of arcs. Linear Algebra Appl., 2011, 434（5）, 1215-1227], authors conjectured that D is the underlying digraph of S with exp（D）= 3 if and only if D is isomorphic to EDn,3,3, where EDn,3,3 = （V, A） is a digraph with V = {1, 2,..., n}, A = {（1, i）, （i, 1） [ 3 〈： i 〈 n} U {（2i - 1, 2i）, （2i, 2i - 1） [ 2 〈 〈 2} U {（2, 3）, （3, 2）, （2, 4）, （4, 2）}）. In this paper, we show the conjecture is true and completely characterize the underlying digraphs which have base 3 and the minimum number of arcs.
文摘Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in SDG generated from chemical process. From the point of the inherent operability, the worst unsafe factor is the SDG having positive loops that means any disturbance occurring within the loop will propagate through the nodes one by one and are amplified gradually, so the system may lose control, which may lead to an accident. So finding the positive loops in a SDG and treating these unsafe factors in a proper manner can improve the inherent safety of a chemical process. This article proposed a method that can detect the above-mentioned unsafe factors in the proc- ess conceptual design stage automatically through the analysis of the SDG generated from the chemical process. A case study is illustrated to show the working of the algorithm, and then a complicated case from industry is studied to depict the effectiveness of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1090106111071088)the Zhujiang Technology New Star Foundation of Guangzhou(Grant No.2011J2200090)
文摘In this paper, we study the bases and base sets of primitive symmetric loop-free （generalized） signed digraphs on n vertices. We obtain sharp upper bounds of the bases, and show that the base sets of the classes of such digraphs are （2, 3,..., 2n - 1}. We also give a new proof of an important result obtained by Cheng and Liu.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA110503-3)Fundamental Research Funds for the Central Universities of China(Grant No.2860219030)Foundation of Traction Power State Key Laboratory of Southwest Jiaotong University,China(Grant No.TPL1308)
文摘Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.
基金Supported by the National Natural Science Foundation of China(Grant No.12071260)。
文摘A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72371031,62173065,62476045)Fundamental Research Funds for the Central Universities(Grant No.124330008)。
文摘The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to address this issue.However,there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures.To support developers,researchers,and practitioners in this field,we introduce a Python library named SNSAlib(Signed Network Structure Analysis),specifically designed to meet these analytical requirements.This library encompasses empirical signed network datasets,signed null model algorithms,signed statistics algorithms,and evaluation indicators.The primary objective of SNSAlib is to facilitate the systematic analysis of micro-and meso-structure features within signed networks,including node popularity,clustering,assortativity,embeddedness,and community structure by employing more accurate signed null models.Ultimately,it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.
文摘This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
文摘In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
文摘The 2-sum of two digraphs and , denoted , is the digraph obtained from the disjoint union of and by identifying an arc in with an arc in . A digraph D is supereulerian if D contains a spanning eulerian subdigraph. It has been noted that the 2-sum of two supereulerian (or even hamiltonian) digraphs may not be supereulerian. We obtain several sufficient conditions on and for to be supereulerian. In particular, we show that if and are symmetrically connected or partially symmetric, then is supereulerian.
基金The NSF(11271365)of Chinathe NSF(BK20151117)of Jiangsu Province
文摘A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.
文摘Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1176107161363020)+1 种基金Science and Technology Innovation Project of Xinjiang Normal University(Grant No.XSY201602013)the"13th Five-Year"Plan for Key Discipline Mathematics of Xinjiang Normal University(Grant No.17SDKD1107)
文摘A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.
