摘要
The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Fn be the set of all trees of order n. In this paper, we will provide the ordering of trees in 3n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al. [The ordering of trees and connected graphs by algebraic connectivity. Linear Algebra Appl., 428, 1421-1438 （2008）].
Abstract The algebraic connectivity of a graph G is the second smallest eigenvalue of its Laplacian matrix. Let Fn be the set of all trees of order n. In this paper, we will provide the ordering of trees in 3n up to the last eight trees according to their smallest algebraic connectivities when n ≥ 13. This extends the result of Shao et al. [The ordering of trees and connected graphs by algebraic connectivity. Linear Algebra Appl., 428, 1421-1438 （2008）].
基金
Supported by FRG, Hong Kong Baptist University, National Science Foundation (NSF) of China (Grant Nos.10871204, 11101358)
NSF of Fujian (Grant Nos. 2011J05014, 2011J01026)
Project of Fujian Education Department (Grant No. JA11165)
Fundamental Research Funds for the Central Universities (Grant No. 09CX04003A)
Research Fund of Zhangzhou Normal University (Grant No. SJ1004)
