## Largest Known (Degree, Diameter)-Graphs

### Diameter 3

last modification: November 1, 2005.
http://www-mat.upc.es/grup_de_grafs/desc_g.html

**C5 x F4**
Degree=** 3**, Diam=** 3**; N=**20**; Moore bound=22;
**optimal**
A description in: 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
Download a Cabri text file of C5xF4.

**Allwr**
Delta= **4**, Diam= **3**; N=**41**; Moore bound=53;
Graphs found by
James Allwright
(School of Computer Science, University of Westminster) by using a
heuristic
algorithm. 13 different graphs with 41 vertices were found
J. Allwright, New (Delta, D) graphs discovered by heuristic search.
* Discrete Applied Mathematics *, ** 37/38** (1992), pp. 3--8.
Download a adjacecy list of
*Allwr*

**Exoo_72**
Delta= **5**, Diam= **3**; N=**72**; Moore bound=106;
Download the Cabri text file of the graph.
Download the adjacency list of the graph.

**Exoo_111**
Delta= **6**, Diam= **3**; N=**111**; Moore bound=187;
Download the adjacency list of the graph.

**Exoo_168**
Delta= **7**, Diam= **3**; N=**168**; Moore bound=302;
Download the adjacency list
of the graph.

**CM_253**
Degree= **8**, Diameter = **3**; Order =**253**;
Moore bound=457.
Obtained (June 1994) as a Cayley graph for semidirect product of Zm with Zn.
Group Generators Inverses Order of Generator
11*(9)23 [7 2] [4 11]
[10 4] [1 10]
[1 16] [10 11]
[9 17] [2 3]
Comellas, F.; Mitjana M. In preparation (1995).
Download the adjacency list
of the graph.
--------------------
Also obtained in January 1997 as a Cayley graph for semidirect product of Zm with Zn.
11*(3)23 4,0 7,0 3,9 8,15 2,10 9, 2,15 9,6
M. Sampels (Sampels@Informatik.Uni-Oldenburg.DE). Large networks with
small diameter. (In preparation)