## Abstract A Steinhaus graph is a graph with __n__ vertices whose adjacency matrix (__a__~i, j~) satisfies the condition that __a__~i, j~ ο£½ __a__~aββ1, jββ1~ + __a__ ~iββ1, j~ (mod 2) for each 1 < __i__ < __j__ β€ __n__. It is clear that a Steinhaus graph is determined by its first row. In [3] Brin
Almost all Cayley graphs have diameter 2
β Scribed by Jixiang Meng; Qiongxiang Huang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 118 KB
- Volume
- 178
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We prove that almost all Cayley graphs have diameter 2.
π SIMILAR VOLUMES
Let T be a tree on n vertices, and let E <$ be a small fixed positive number. The tribe number t&) of T is the smallest integer r such that when any vertex is deleted, some r or fewer subtrees in the resulting forest together contain more than (1-e)n vertices. We prove the following, theorem: Almost
## Abstract ErdΓΆs proved that there exist graphs of arbitrarily high girth and arbitrarily high chromatic number. We give a different proof (but also using the probabilistic method) that also yields the following result on the typical asymptotic structure of graphs of high girth: for all βββ₯β3 and