在文献Ji-Ming Guo,Shang-Wang Tan.A conjecture on the second largest eigenvalue of a tree with perfect matchings.Linear Algebra and its Applications,2002,347(1-3):9-15和Ji-Ming Guo,Shang-Wang Tan.A note on the second largest eigenvalue of a tree with perfect matchings.Linear Algebra and Its Applications,2004,380:125-134中,Guo和Tan给出了有2k个顶点且有完美匹配的树的第二大特征值的上界,这个上界与顶点数有关,并且刻画了第二大特征值达到该上界的树.本文给出了有2k个顶点的树的第二大特征值的上界,这个上界与顶点数和最大匹配的基数有关,并且刻画了第二大特征值达到该上界的树.
