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

作　　者：刘晓蓉[1,2] 张荣[2] 

机构地区：[1]青海师范大学数学系,青海西宁810008 [2]盐城师范学院数学与统计学院,江苏盐城224002

出　　处：《盐城工学院学报（自然科学版）》2015年第4期11-14,共4页Journal of Yancheng Institute of Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11171290);江苏省自然科学基金(BK20151295)

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。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- 2and 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.

关 键 词：非二部单圈图 悬挂点 最小特征值 

分 类 号：O157.5[理学—数学]