The six classes of trees with the largest algebraic connectivity |
| |
Authors: | Xi-Ying Yuan Li Zhang |
| |
Institution: | Department of Mathematics, Tongji University, Shanghai 200092, China |
| |
Abstract: | In this paper, we study the algebraic connectivity α(T) of a tree T. We introduce six Classes (C1)-(C6) of trees of order n, and prove that if T is a tree of order n?15, then if and only if , where the equality holds if and only if T is a tree in the Class (C6). At the same time we give a complete ordering of the trees in these six classes by their algebraic connectivity. In particular, we show that α(Ti)>α(Tj) if 1?i<j?6 and Ti is any tree in the Class (Ci) and Tj is any tree in the Class (Cj). We also give the values of the algebraic connectivity of the trees in these six classes. As a technique used in the proofs of the above mentioned results, we also give a complete characterization of the equality case of a well-known relation between the algebraic connectivity of a tree T and the Perron value of the bottleneck matrix of a Perron branch of T. |
| |
Keywords: | 05C50 |
本文献已被 ScienceDirect 等数据库收录! |
|