The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An ...The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.展开更多
Abstract： Research on the ecological species groups and interspecific association of plant species are helpful to discover species coexistence processes and mechanisms, and to more fully understand plant community st...Abstract： Research on the ecological species groups and interspecific association of plant species are helpful to discover species coexistence processes and mechanisms, and to more fully understand plant community structure, function, and its taxonomy. However, little is known about the ecological species groups （ESG） and the interspecific association of dominant species in Daiyun Mountain National Nature Reserve of Fujian Province, China. Therefore, the main goal of this paper is to explore the ESG using maximal tree, and to analyze interspecific associations of 32 dominant species selected from lo2 sample plots using the chi-square test. The results show that： （1） 32 dominant species have a significant overall positive interspecific association, which indicates that the natural forest in Daiyun Mountain National Nature Reserve is stable, （a） The species pairs with weak associations, non-associations and positive associations account for lo.88%, 29.64% and 59.48% of the total 496 species pairs respectively, which suggests that the population distributions of the dominant species investigated are relatively independent, （3） The following species pairs may be useful for practical application, 〈Pinus taiwanensis, Rhododendron farrerae〉, 〈Castanopsis carlesii, Altingia chinensis〉, 〈C. carlesii, Castanopsis fargesii〉, 〈Castanopsis eyrei, C. fargesii〉, 〈P. taiwanensis, Fagus lucida〉 , 〈Machilus thunbergii, Castanopsis nigrescens〉, and （4） The results of clustering analysis based on the maximal tree method indicates that the 32 dominant species can be divided into 3 ESGs when A at o.6o, that is ESG I {Pinus massoniana, Cunning hamia lanceolata}, ESG II {P. taiwanensis, R. farrerae, Enkianthus quinqueflorus}, ESG III {C. carlesii, A. chinensis, C. eyrei, Castanopsis fabri, C. fargesii, Schima superba, Machilus thunbergii, Rhododendron latoueheae}. The results may be used for the selection of afforestation tree species in South China Forest Areas and guide the natural manag展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471131)the Natural Science Foundation of Zhejiang Province(Grant No.102055).
文摘The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.
基金supported by a grant from the Fujian Provincial Natural Science Foundation(2014J01380)Study Abroad for Young Scholar of China Scholarship Council (201307870056)Youth Foundation of Fujian Agriculture and Forestry University (k13xjj08a)
文摘Abstract： Research on the ecological species groups and interspecific association of plant species are helpful to discover species coexistence processes and mechanisms, and to more fully understand plant community structure, function, and its taxonomy. However, little is known about the ecological species groups （ESG） and the interspecific association of dominant species in Daiyun Mountain National Nature Reserve of Fujian Province, China. Therefore, the main goal of this paper is to explore the ESG using maximal tree, and to analyze interspecific associations of 32 dominant species selected from lo2 sample plots using the chi-square test. The results show that： （1） 32 dominant species have a significant overall positive interspecific association, which indicates that the natural forest in Daiyun Mountain National Nature Reserve is stable, （a） The species pairs with weak associations, non-associations and positive associations account for lo.88%, 29.64% and 59.48% of the total 496 species pairs respectively, which suggests that the population distributions of the dominant species investigated are relatively independent, （3） The following species pairs may be useful for practical application, 〈Pinus taiwanensis, Rhododendron farrerae〉, 〈Castanopsis carlesii, Altingia chinensis〉, 〈C. carlesii, Castanopsis fargesii〉, 〈Castanopsis eyrei, C. fargesii〉, 〈P. taiwanensis, Fagus lucida〉 , 〈Machilus thunbergii, Castanopsis nigrescens〉, and （4） The results of clustering analysis based on the maximal tree method indicates that the 32 dominant species can be divided into 3 ESGs when A at o.6o, that is ESG I {Pinus massoniana, Cunning hamia lanceolata}, ESG II {P. taiwanensis, R. farrerae, Enkianthus quinqueflorus}, ESG III {C. carlesii, A. chinensis, C. eyrei, Castanopsis fabri, C. fargesii, Schima superba, Machilus thunbergii, Rhododendron latoueheae}. The results may be used for the selection of afforestation tree species in South China Forest Areas and guide the natural manag
