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
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.
