The number of graphs of given diameter
Combinatorics
2012-04-23 v1
Abstract
In this paper it is proved that there are constants 0< c_2< c_1 such that an asymptotic formula can be given for the the number of (labeled) n-vertex graphs of diameter d whenever n tends to infinity and 2 < d < n - c_1 (log n). A typical graph of diameter d consists of a combination of an induced path of length d and a highly connected block of size n-d+3. In the case d > n- c_2(log n) another asymptotic formula is calculated and the typical graph has a completely different snakelike structure.
Keywords
Cite
@article{arxiv.1204.4580,
title = {The number of graphs of given diameter},
author = {Zoltan Furedi and Younjin Kim},
journal= {arXiv preprint arXiv:1204.4580},
year = {2012}
}
Comments
13 pages