| 圈与路相交的图的最大特征值 |
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| 引用本文： | 任秋道. 圈与路相交的图的最大特征值[J]. 内江师范学院学报, 2009, 24(10): 26-29,54 |
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| 作者姓名： | 任秋道 |
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| 作者单位： | 绵阳师范学院数学与信息科学系,四川,绵阳,621000 |
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| 基金项目： | 四川省教育厅自然科学基金 |
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| 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Cili2…il（Pk1，Pk2，…，Pkl），1≤ij≤m，1≤j≤l．顶点vm悬挂l条Pk1，Pk2，…，Rkl的图简记为Cm^l（Pk1，Pk2，…，Pkl）．在圈C=v1v2…vmv1的顶点i，上悬挂l条路Pkl，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λ1（Gi1^l（Pk1，Pk2，…，Pkl））≥λ1（Ci1i2…il（Pk1,Pk2,…Pkl），1≤ij≤m-1，j=1，2，…，l．
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| 关 键 词： | 邻接矩阵 特征多项式 特征值 圈 |
On the Maximum Eigenvalues of Graphs with Intersectant Cycles and Paths |
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| REN Qiu-dao. On the Maximum Eigenvalues of Graphs with Intersectant Cycles and Paths[J]. Journal of Neijiang Teachers College, 2009, 24(10): 26-29,54 |
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| Authors: | REN Qiu-dao |
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| Affiliation: | REN Qiu-dao (Department of Mathematics＆ Information Science , Mianyang Normal University, Mianyang , Sichuan 621000, China) |
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| Abstract: | 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, |
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| Keywords: | adjacent matrix characteristic polynomial eigenvalue cycle |
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