Let vt(d, 2) be the largest order of a vertex-transitive graph of degree d and diameter 2. It is known that vt(d, 2)=d 2 +1 for d=1, 2, 3, and 7; for the remaining values of d we have vt(d, 2) d 2 &1. The only known general lower bound on vt(d, 2), valid for all d, seems to be vt(d, 2) w(d+2)ร2x W(d
A note on diameter and the degree sequence of a graph
โ Scribed by Simon Mukwembi
- Book ID
- 113449238
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 224 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract We investigate a family of graphs relevant to the problem of finding large regular graphs with specified degree and diameter. Our family contains the largest known graphs for degree/diameter pairs (3, 7), (3, 8), (4, 4), (5, 3), (5, 5), (6, 3), (6, 4), (7, 3), (14, 3), and (16, 2). We a
We show that the joint distribution of the degrees of a random graph can be accurately approximated by several simpler models derived from a set of independent binomial distributions. On the one hand, we consider the distribution of degree sequences of 1 random graphs with n vertices and m edges. Fo