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| 最小Q-特征值第二小的给定悬挂点数的非二部单圈图 |
| The Non-bipartite Unicyclic Graph with Fixed Number of Pendent Vertices Whose Least Q-eigenvalue Attains the Second Smallest |
| 投稿时间：2015-05-20 |
| DOI：10.16018/j.cnki.cn32-1650/n.201504003最小Q-特征值第二小的给定悬挂点数的非二部单圈图 |
| 中文关键词: 非二部单圈图 悬挂点 最小特征值 |
| 英文关键词: Non-bipartite unicyclic graph Pendant vertices Least eigenvalue |
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| 摘要点击次数: 5156 |
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| 中文摘要: |
| 图的最小Q-特征值常被用来衡量一个图的非二部程度，受到研究者的广泛关注。在路Pn-k-2的一端接出一个圈C3，另一端接出k个悬挂边，所得的n阶图记为Ukn(3)。范益政等人最近证明Ukn(3)是最小Q-特征值达到最小的图。在他们的基础上，证明C13(n-k-1)是最小Q-特征值达到第二小的图，其中C13(n-k-1)是将Ukn(3)的一条悬挂边移至与悬挂邻点相邻的非悬挂点上所得的图。 |
| 英文摘要: |
| The least Q- eigenvalue of a graph is often used to measure non-bipartiteness of the graph, which is widely concerned by researchers. Let Ukn(3)be the graph of order n which is obtained by attaching a cycle C3 to an end vertex of a path Pn-k-2 and attaching k pendant edges to the other end vertex of the path Pn-k-2. Recently, Yi-Zheng Fan et al. proved that Ukn(3)was the unique graph whose least Q- eigenvalue attained the minimum among all graphs of order n with k pendant vertices. In this paper, we proved that C13(n-k-1) is the unique graph whose least Q- eigenvalue attains the second smallest value, where C13(n-k-1) is the graph obtained from Ukn(3)by relocating a pendant edge to the non-pendant vertex which is adjacent the pendant neighbor. |
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