摘要
设T为具有完美匹配的2q阶树, q(T)为其最小正根.又记Sn为Pn-1的一个邻接悬挂点接出一条新悬挂边而得的n阶树.证明了:若 且 ,q≥4,则 .左边等式成立当且仅当 .右边等式成立当且仅当 .这里Pqq为Pq的每个点都接出一条新悬挂边而得的2q阶树, T*1为S2q-3的三个悬挂点各接出一条新悬挂边而得2q阶树,而T*2则是Sq的每个点都接出一条新悬挂边而得的2q阶树.
Let T be a tree on 2q vertices with a perfect matching, q,(T) be the smallest positive eigenvalue of T. Denoted by Sn the tree with n vertices from the path Pn-1 by joining a new vertex to a neighboring end-vertex on Pn-1. In this paper, we demonstrate that if T P2q, and T Pqq, q≥4, q,(T*1)≤q,(T)≤q,(T*2), and the lower bound occurs only when T T*1 while the upper bound occurs only when T T*2, where Pqq is the tree from Pq by joining a new vertex to each vertex in Pn; T*1 is the tree from S2q-3by joining a new vertex to each end -vertex in S2q-3; and T*2 is the tree from Sq, by joining a new vertex to each vertex in Sq.
出处
《湖州师范学院学报》
2000年第3期5-9,共5页
Journal of Huzhou University
关键词
最小正根
完美匹配
树
界
简单图
特征多项式
tree, eigenvalue, perfect matching, smallest positive eigenvalue