A Universal upper bound on Graph Diameter based on Laplacian Eigenvalues
Discrete Mathematics
2012-12-13 v1 Combinatorics
Probability
Abstract
We prove that the diameter of any unweighted connected graph G is O(k log n/lambda_k), for any k>= 2. Here, lambda_k is the k smallest eigenvalue of the normalized laplacian of G. This solves a problem posed by Gil Kalai.
Keywords
Cite
@article{arxiv.1212.2701,
title = {A Universal upper bound on Graph Diameter based on Laplacian Eigenvalues},
author = {Shayan Oveis Gharan and Luca Trevisan},
journal= {arXiv preprint arXiv:1212.2701},
year = {2012}
}