A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which i...A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.展开更多
In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tr...In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.展开更多
The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that ther...The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.展开更多
Fault diagnostics is important for safe operation of nuclear power plants(NPPs). In recent years, data-driven approaches have been proposed and implemented to tackle the problem, e.g., neural networks, fuzzy and neuro...Fault diagnostics is important for safe operation of nuclear power plants(NPPs). In recent years, data-driven approaches have been proposed and implemented to tackle the problem, e.g., neural networks, fuzzy and neurofuzzy approaches, support vector machine, K-nearest neighbor classifiers and inference methodologies. Among these methods, dynamic uncertain causality graph(DUCG)has been proved effective in many practical cases. However, the causal graph construction behind the DUCG is complicate and, in many cases, results redundant on the symptoms needed to correctly classify the fault. In this paper, we propose a method to simplify causal graph construction in an automatic way. The method consists in transforming the expert knowledge-based DCUG into a fuzzy decision tree(FDT) by extracting from the DUCG a fuzzy rule base that resumes the used symptoms at the basis of the FDT. Genetic algorithm(GA) is, then, used for the optimization of the FDT, by performing a wrapper search around the FDT: the set of symptoms selected during the iterative search are taken as the best set of symptoms for the diagnosis of the faults that can occur in the system. The effectiveness of the approach is shown with respect to a DUCG model initially built to diagnose 23 faults originally using 262 symptoms of Unit-1 in the Ningde NPP of the China Guangdong Nuclear Power Corporation. The results show that the FDT, with GA-optimized symptoms and diagnosis strategy, can drive the construction of DUCG and lower the computational burden without loss of accuracy in diagnosis.展开更多
文摘A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.
文摘In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.
文摘The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.
文摘Fault diagnostics is important for safe operation of nuclear power plants(NPPs). In recent years, data-driven approaches have been proposed and implemented to tackle the problem, e.g., neural networks, fuzzy and neurofuzzy approaches, support vector machine, K-nearest neighbor classifiers and inference methodologies. Among these methods, dynamic uncertain causality graph(DUCG)has been proved effective in many practical cases. However, the causal graph construction behind the DUCG is complicate and, in many cases, results redundant on the symptoms needed to correctly classify the fault. In this paper, we propose a method to simplify causal graph construction in an automatic way. The method consists in transforming the expert knowledge-based DCUG into a fuzzy decision tree(FDT) by extracting from the DUCG a fuzzy rule base that resumes the used symptoms at the basis of the FDT. Genetic algorithm(GA) is, then, used for the optimization of the FDT, by performing a wrapper search around the FDT: the set of symptoms selected during the iterative search are taken as the best set of symptoms for the diagnosis of the faults that can occur in the system. The effectiveness of the approach is shown with respect to a DUCG model initially built to diagnose 23 faults originally using 262 symptoms of Unit-1 in the Ningde NPP of the China Guangdong Nuclear Power Corporation. The results show that the FDT, with GA-optimized symptoms and diagnosis strategy, can drive the construction of DUCG and lower the computational burden without loss of accuracy in diagnosis.
