MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


I am interested in upper bounding the second largest eigenvalue of the adjacency matrix of a graph $T$ with the following property: 1. $T$ contains self loops. 2. $T$ contains multiple edges (of, alternatively, is a weighted graph). 3. $T$ has a structure of a perfect binary tree (with self loops in every vertex).

The eigenvalue bounds that arise from edge expansion and vertex expansion are too weak for the bound I am trying to prove. How would you suggest dealing with weighted binary trees?

Thank you.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.