## Largest Known (Degree, Diameter)-Graphs

### Diameter 4

Last modification: July 30, 2006.
http://www-mat.upc.es/grup_de_grafs/desc_g.html

**vC, AFY**
Delta=** 3**, Diam=** 4**; N=**38**; Moore bound=46;
**optimal**
Described independently in:

- von Conta, C; Torus and other networks as communication
networks with up to some hundred points;
*IEEE Trans Comp*,**c-32** (1983), pp. 657-666.
- Alegre, I.; Fiol, M.A. and Yebra, J.L.A;
Some large graphs with given degree and diameter;
*J. Graph Theory*,**10** (1986), pp.219-224.

The proof of optimality appeared in:

Dominique Buset;
Maximal cubic graphs with diameter 4; * Discrete Math.*,**101** (2000), pp. 53--61.

**Exoo-98**
Delta= **4**, Diam= **4**; N=**98**; Moore bound=161;
*Exoo_98*
Download the adjacency list of the graph.

**Exoo-212**
Delta= **5**, Diam= **4**; N=**212**; Moore bound=426;
Download the adjacency list of the graph.

**Loz_390**
Degree= **6**, Diameter = **4**; Order =**390**; Moore
bound=937
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Download the adjacency list of the graph.
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.

**S_672**
Degree= **7**, Diameter = **4**; Order =**672**; Moore bound=1814
Obtained as a Cayley graph for semidirect product of Zm with Zn
6*(39) 112 2,73 4,23 5,54 1,22 5,71 1,31 3,42
M. Sampels. In: Rolf H. Möhring (Ed.): 23rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG '97), Lecture Notes in Computer Science 1335, pp. 288-302, Springer-Verlag, 1997
ISBN 3-540-63757-5

**Loz_1100**
Degree= **8**, Diameter = **4**; Order =**1100**;
Moore bound=3201
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Download the adjacency list of the graph.
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.

**Loz_1550**
Degree= **9**, Diameter = **4**; Order =**1550**;
Moore bound=5266.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Download the adjacency list of the graph.
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.

**Loz_2223**
Degree= **10**, Diameter = **4**; Order =**2223**;
Moore bound=8201.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Download the adjacency list of the graph.
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.