In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
An induced matching M in a graph G is a matching such that V(M) induces a1-regular subgraph of G. The induced matching number of a graph G, denoted by IM(G), isthe maximum number r such that G has an induced matching ...An induced matching M in a graph G is a matching such that V(M) induces a1-regular subgraph of G. The induced matching number of a graph G, denoted by IM(G), isthe maximum number r such that G has an induced matching of r edges. Induced matchingnumber of Prn x Pn is investigated in this paper. The main results are as follows:展开更多
Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M...Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.展开更多
本文考虑决策者在实际问题中存有的多种决策心理,针对毕达哥拉斯模糊偏好下考虑双边主体损失规避和参照依赖心理行为的双边匹配问题提出一种决策方法。对于双边主体给出的毕达哥拉斯模糊偏好信息,依据TODIM(Tomada de Decisao Interativ...本文考虑决策者在实际问题中存有的多种决策心理,针对毕达哥拉斯模糊偏好下考虑双边主体损失规避和参照依赖心理行为的双边匹配问题提出一种决策方法。对于双边主体给出的毕达哥拉斯模糊偏好信息,依据TODIM(Tomada de Decisao Interativa Multicritério)思想获得双边主体相较于另一边匹配主体的总体优势度,进而构建双边主体的满意度矩阵;而后,在考虑双边主体一对一的数量匹配约束下,以实现双边主体满意度最大化为决策目标,建立多目标双边匹配决策模型;最后,通过线性加权法进一步将其转化为单目标双边匹配模型,通过模型求解获得最优双边匹配方案;一个实际供应链管理系统软件的交易匹配算例验证本方法的可行性和有效性。展开更多
针对北斗三号(BeiDou-3 Navigation Satellite System,BDS-3)PPP-B2b信号精密单点定位(precise point positioning,PPP)服务可用性,以改正参数的可用性比例、平均可用卫星数和改正参数匹配性为指标进行了系统分析.结果表明:在中国及周...针对北斗三号(BeiDou-3 Navigation Satellite System,BDS-3)PPP-B2b信号精密单点定位(precise point positioning,PPP)服务可用性,以改正参数的可用性比例、平均可用卫星数和改正参数匹配性为指标进行了系统分析.结果表明:在中国及周边地区,BDS-3 PPP-B2b信号改正参数的可用性在71%~95%,且在北京地区达到最大,GPS改正参数可用性在68.5%~88.6%,差于BDS-3.中国及周边地区用户缺少PPP-B2b信号改正参数的卫星观测弧段主要集中在低高度角时段,其改正参数的可用性随着截止高度角的增大而增大;BDS-3、GPS和BDS-3/GPS在中国及周边地区的改正数可用平均卫星数分别约为8颗、7颗和15颗,可以确保有效的实时PPP(real time PPP,RT-PPP)服务性能,但平均约有1颗BDS-3卫星和2颗GPS卫星因为缺少PPP-B2b信号改正参数而无法参与RT-PPP服务;对于赤道以南地区,单个系统基本无法提供有效的PPPB2b服务,其改正参数的平均可用性低于50%,但BDS-3/GPS双系统在部分低纬度地区可提供约7~11颗的可用卫星;由于轨道改正参数和钟差改正参数更新频率不一致,在钟差改正数版本号(IOD Corr)参数更新时,会出现短暂的改正参数不匹配情况.展开更多
ErdOs,Gimbel and Straight （1990） conjectured that if ω（G）〈5 and z（G）〉3,then z（G）≥Z（G）-2. But by using the concept of edge cochromatic number it is proved that if G is the line graph of a connected triang...ErdOs,Gimbel and Straight （1990） conjectured that if ω（G）〈5 and z（G）〉3,then z（G）≥Z（G）-2. But by using the concept of edge cochromatic number it is proved that if G is the line graph of a connected triangle-free graph with ω（G）〈5 and G≠K4, then z（G）≥X（G）-2.展开更多
A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mix...A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mixed graph G^(-) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of G^(-) , respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.展开更多
A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings ...A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
文摘An induced matching M in a graph G is a matching such that V(M) induces a1-regular subgraph of G. The induced matching number of a graph G, denoted by IM(G), isthe maximum number r such that G has an induced matching of r edges. Induced matchingnumber of Prn x Pn is investigated in this paper. The main results are as follows:
文摘Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.
文摘本文考虑决策者在实际问题中存有的多种决策心理,针对毕达哥拉斯模糊偏好下考虑双边主体损失规避和参照依赖心理行为的双边匹配问题提出一种决策方法。对于双边主体给出的毕达哥拉斯模糊偏好信息,依据TODIM(Tomada de Decisao Interativa Multicritério)思想获得双边主体相较于另一边匹配主体的总体优势度,进而构建双边主体的满意度矩阵;而后,在考虑双边主体一对一的数量匹配约束下,以实现双边主体满意度最大化为决策目标,建立多目标双边匹配决策模型;最后,通过线性加权法进一步将其转化为单目标双边匹配模型,通过模型求解获得最优双边匹配方案;一个实际供应链管理系统软件的交易匹配算例验证本方法的可行性和有效性。
文摘针对北斗三号(BeiDou-3 Navigation Satellite System,BDS-3)PPP-B2b信号精密单点定位(precise point positioning,PPP)服务可用性,以改正参数的可用性比例、平均可用卫星数和改正参数匹配性为指标进行了系统分析.结果表明:在中国及周边地区,BDS-3 PPP-B2b信号改正参数的可用性在71%~95%,且在北京地区达到最大,GPS改正参数可用性在68.5%~88.6%,差于BDS-3.中国及周边地区用户缺少PPP-B2b信号改正参数的卫星观测弧段主要集中在低高度角时段,其改正参数的可用性随着截止高度角的增大而增大;BDS-3、GPS和BDS-3/GPS在中国及周边地区的改正数可用平均卫星数分别约为8颗、7颗和15颗,可以确保有效的实时PPP(real time PPP,RT-PPP)服务性能,但平均约有1颗BDS-3卫星和2颗GPS卫星因为缺少PPP-B2b信号改正参数而无法参与RT-PPP服务;对于赤道以南地区,单个系统基本无法提供有效的PPPB2b服务,其改正参数的平均可用性低于50%,但BDS-3/GPS双系统在部分低纬度地区可提供约7~11颗的可用卫星;由于轨道改正参数和钟差改正参数更新频率不一致,在钟差改正数版本号(IOD Corr)参数更新时,会出现短暂的改正参数不匹配情况.
基金Supported by the Natural Science Foundation of Gansu Province (3ZS051-A25-025).
文摘ErdOs,Gimbel and Straight （1990） conjectured that if ω（G）〈5 and z（G）〉3,then z（G）≥Z（G）-2. But by using the concept of edge cochromatic number it is proved that if G is the line graph of a connected triangle-free graph with ω（G）〈5 and G≠K4, then z（G）≥X（G）-2.
基金the National Natural Science Foundation of China (Nos. 11971054 and 12161141005)the Fundamental Research Funds for the Central Universities (No. 2016JBM071)。
文摘A mixed graph G^(-) is obtained by orienting some edges of G, where G is the underlying graph of G^(-) . The positive inertia index, denoted by p~+( G), and the negative inertia index, denoted by n~-(G^(-) ), of a mixed graph G^(-) are the integers specifying the numbers of positive and negative eigenvalues of the Hermitian adjacent matrix of G^(-) , respectively. In this paper, the positive and negative inertia indices of the mixed unicyclic graphs are studied. Moreover, the upper and lower bounds of the positive and negative inertia indices of the mixed graphs are investigated, and the mixed graphs which attain the upper and lower bounds are characterized respectively.
基金This work is supported by the Science and Technology Program of Guangzhou,China(No.202002030183)the Guangdong Province Natural Science Foundation(No.2021A1515012045)the Qinghai Province Natural Science Foundation(No.2020-ZJ-924).
文摘A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.
