A conjecture on the second largest eigenvalue of a tree with perfect matchings

摘要

In this paper, we investigated a conjecture [Linear Algebra Appl. 283 (1998) 247] about the upper bounds of the second largest eigenvalue lambda(2)(T) of a tree T with perfect matchings, and proved that the second part of the conjecture is true but the first part of the conjecture is not true. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 7]