“一星多用、多星组网、多网协同”思想的发展与应用为卫星互联网的关键节点识别带来了更多的挑战,也提出了更高的要求。针对卫星时序网络节点评估结果不准确的问题,考虑了不同时间片拓扑之间的耦合强度,提出了一种基于改进超邻接矩阵(s...“一星多用、多星组网、多网协同”思想的发展与应用为卫星互联网的关键节点识别带来了更多的挑战,也提出了更高的要求。针对卫星时序网络节点评估结果不准确的问题,考虑了不同时间片拓扑之间的耦合强度,提出了一种基于改进超邻接矩阵(supra-adjacency matrix,SAM)的卫星互联网时序网络模型。随后,综合卫星节点在网络中固有的拓扑特性和通信特性,选取特征向量中心性、介数中心性、节点紧密度、传输时延、传输速率和传输容量指标建立了节点重要度综合评估指标体系,在此基础上,基于熵权-逼近理想解排序法(technique for order preference by similarity to an ideal solution,TOPSIS)和时间权重矩阵设计了卫星互联网节点重要度评估方法。通过ARPANET和铱星星座进行仿真验证,实验结果证明了所提出的模型和方法能够准确地从局部和全局角度获得卫星节点重要度排序,并识别出潜在重要节点,对卫星互联网关键节点识别及抗毁性研究有一定的参考意义。展开更多
A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S i...A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.展开更多
树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)...树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.展开更多
文摘“一星多用、多星组网、多网协同”思想的发展与应用为卫星互联网的关键节点识别带来了更多的挑战,也提出了更高的要求。针对卫星时序网络节点评估结果不准确的问题,考虑了不同时间片拓扑之间的耦合强度,提出了一种基于改进超邻接矩阵(supra-adjacency matrix,SAM)的卫星互联网时序网络模型。随后,综合卫星节点在网络中固有的拓扑特性和通信特性,选取特征向量中心性、介数中心性、节点紧密度、传输时延、传输速率和传输容量指标建立了节点重要度综合评估指标体系,在此基础上,基于熵权-逼近理想解排序法(technique for order preference by similarity to an ideal solution,TOPSIS)和时间权重矩阵设计了卫星互联网节点重要度评估方法。通过ARPANET和铱星星座进行仿真验证,实验结果证明了所提出的模型和方法能够准确地从局部和全局角度获得卫星节点重要度排序,并识别出潜在重要节点,对卫星互联网关键节点识别及抗毁性研究有一定的参考意义。
基金Supported by NSFC(Grant Nos.11801148 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。
文摘A{(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)^(2),S_(12)^(2),S_(12)^(4),S_(12)^(5),S_(14)^(3),S_(14)^(5),S_(16)^(3),S_(18)^(5),S_(24)as shown in Fig.1.As a corollary,it is shown that if a{(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.
文摘树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.
