圈与路相交的图的最大特征值  

On the Maximum Eigenvalues of Graphs with Intersectant Cycles and Paths

作　　者：任秋道[1] 

机构地区：[1]绵阳师范学院数学与信息科学系,四川绵阳621000

出　　处：《内江师范学院学报》2009年第10期26-29,54,共5页Journal of Neijiang Normal University

基　　金：四川省教育厅自然科学基金(07114931)资助项目

摘　　要：设圈C=v1v2…vmv1,m≥3.在圈C的顶点vi1,vi2,…,vil分别悬挂一条路Pk1,Pk2,…,Pkl的图记为Ci1i2…il(Pk1,Pk2,…,Pkl),1≤ij≤m,1≤j≤l.顶点vm悬挂l条路Pk1,Pk2,…,Pkl的图简记为Cml(Pk1,Pk2,…,Pkl).在圈C=v1v2…vmv1的顶点i1上悬挂l条路Pk1,Pk2,…,Pkl的图的最大特征值不小于将l条路分别悬挂在l个顶点i1,i2,…,il的图的最大特征值,即1λ(Cil1(Pk1,Pk2,…,Pkl))≥1λ(Ci1i2…il(Pk1,Pk2,…,Pkl)),1≤ij≤m-1,j=1,2,…,l.Let a cycle be C=v1v2…vmv1,m≥3, attach pendent paths Pk1,Pk2,…,Pkl to the vertices vi1,vi2,…,vil of C, respectively. Record such a graph as Cili2…il（Pk1,Pk2,…,Pkl）,1≤ij≤m,1≤j≤l and for the graph at whose vertice vm there exist l new paths Pk1,Pk2,…,Pkl it is concisely recorded as Cml （ Pk1,Pk2,…,Pkl） Our research finds that for a graph at whose vertice i1 of C=v1v2…vmv1 there exist 1 paths Pk1,Pk2,…,Pkl its maximum eigenvalue will be no less than that of the graph in which 1 pendent paths are attached to 1 verticesi,i2 ,… ,il respectively. That is to say, ）.λ1（Gi1^l（Pk1,Pk2,…,Pkl））≥（Ci1i2…il（Pk1,Pk2,…Pkl）,for1≤i≤m-1,

关 键 词：邻接矩阵 特征多项式 特征值 圈 

分 类 号：O175[理学—数学]