Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powe...Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.展开更多
It is well known that the eigenvalues of a strongly regular graph with parameters(n,k,a,c),are k and the two roots of the quadratic equation x^2-(a-c)x-(k-c)=0.And the multiplicities can be determined.This gives an al...It is well known that the eigenvalues of a strongly regular graph with parameters(n,k,a,c),are k and the two roots of the quadratic equation x^2-(a-c)x-(k-c)=0.And the multiplicities can be determined.This gives an alternative method of determined its spectra,this article is based on one typical strongly regular graph K_(m(r)).展开更多
设G是阶为n边数为m的简单图,λ1,λ2,…,λn是G的邻接矩阵的特征值,μ1,μ2,…,μn是G的拉普拉斯矩阵的特征值.图G的能量定义为E(G)=sum from i=1 to n|λi|,拉普拉斯能量LE(G)=sum from i=1 to n|μi-(2m/n)|.利用代数和图论的方法,得...设G是阶为n边数为m的简单图,λ1,λ2,…,λn是G的邻接矩阵的特征值,μ1,μ2,…,μn是G的拉普拉斯矩阵的特征值.图G的能量定义为E(G)=sum from i=1 to n|λi|,拉普拉斯能量LE(G)=sum from i=1 to n|μi-(2m/n)|.利用代数和图论的方法,得到了k-正则图的最大和最小能量,以及最大、最小拉普拉斯能量,并刻划了能量取到最值时对应的图的结构.展开更多
文摘Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.
基金Supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(61272008,11271348,10871189)
基金Supported by Natural Science Foundation of Hebei Province(A2013408009)Natural Science Foundation of Hebei Education Department(ZH2012082)the Doctor Foundation of Langfang Teachers’ College(LSBS201205)
文摘It is well known that the eigenvalues of a strongly regular graph with parameters(n,k,a,c),are k and the two roots of the quadratic equation x^2-(a-c)x-(k-c)=0.And the multiplicities can be determined.This gives an alternative method of determined its spectra,this article is based on one typical strongly regular graph K_(m(r)).
文摘设G是阶为n边数为m的简单图,λ1,λ2,…,λn是G的邻接矩阵的特征值,μ1,μ2,…,μn是G的拉普拉斯矩阵的特征值.图G的能量定义为E(G)=sum from i=1 to n|λi|,拉普拉斯能量LE(G)=sum from i=1 to n|μi-(2m/n)|.利用代数和图论的方法,得到了k-正则图的最大和最小能量,以及最大、最小拉普拉斯能量,并刻划了能量取到最值时对应的图的结构.
