## Largest Known (Degree, Diameter)-Graphs

### Diameter 5

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

**vC, AFY**
Delta=** 3**, Diam=** 5**; N=**70**; Moore bound=94;
Graph obtained by connecting seven clusters like the one shown
in the figure.
The edges are given by *A_(i,j ) <--> B_(i \pm 2^j,j \pm 1)*
for all *i* in *Z/7Z* and *j* in *Z/3Z*.
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

**H'3**
Delta= **4**, Diam= **5**; N=**364**; Moore bound=485;

**Loz_624**
Delta= **5**, Diam= **5**; N=**624**; Moore bound=1706;
Download the adjacency list of the graph.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.

**Loz_1404**
Degree= **6**, Diameter = **5**; Order =**1404**; Moore bound=4687
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.

**DH_2756**
Degree= **7**, Diameter = **5**; Order =**2756**;
Moore bound=10886.
Obtained as a Cayley graph for semidirect product of Zm with Zn.
Group Generators Inverses Order of Generator
52*(2)53 [25 45] [27 37] 52
[30 23] [22 18] 26
[40 39] [12 51] 13
[26 0] 2
Dinneen,M.J. & Hafner,P.; New results for the degree/diameter problem.
*Networks*, **24** (1994) 359-367.

**Loz_5060**
Degree= **8**, Diameter = **5**; Order =**5060**;
Moore bound=22409.
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.

**Al_8268**
Degree= **9**, Diameter = **5**; Order =**8268**; Moore bound=42130.
Communicated by Alexis Rodriguez, Fac. Ing., Univ. Republica, Montevideo (June 2012)
Download the adjacency list of the graph.
.

**Loz_13140**
Degree= **10**, Diameter = **5**; Order =**13140**;
Moore bound=73811.
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_18700**
Degree= **11**, Diameter = **5**; Order =**18700**;
Moore bound=122222.
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_29470**
Degree= **12**, Diameter = **5**; Order =** 29470**; Moore bound=193261.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (August 2006)
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )

**Loz_39576**
Degree= **13**, Diameter = **5**; Order =** 39576**;
Moore bound=.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (August 2006)
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )

**Loz_56790**
Degree= **14**, Diameter = **5**; Order =** 56790**;
Moore bound=433175.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (August 2006)
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )

**Loz_74298**
Degree= **15**, Diameter = **5**; Order =** 74298**;
Moore bound=620566.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (August 2006)
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )