## Largest Known (Degree, Diameter)-Graphs

### Diameter 6

Last modification: August 2, 2006.
http://www-mat.upc.es/grup_de_grafs/desc_g.html

**Exoo_132**
Delta= **3**, Diam= **6**; N=**132**; Moore bound=190;
Download the adjacency list of
the graph.

**H3(K3)**
Delta= **4**, Diam= **6**; N=**740**; Moore bound=1457;
Graph obtained from the generailized hexagon *H*_{3} by replacement
of some of its vertices (see figure) by complete graphs *K*_{3}
F. Comellas and J. Gómez,
New large graphs with given degree and diameter.,
* Graph Theory, Combinatorics and Algorithms, vol 1*,
Yousef Alavi and Allen Schwenk (Eds.), John Wiley & Sons, Inc.;
New York (1995) pp. 221-233.
ISBN 0-471-30437-9.
(Proc. of the Seventh Quadrennial International Conference on the Theory and
Applications of Graphs, Kalamazoo, MI, USA, June 1992.)

**H_4(K_3)**
Delta= **5**, Diam= **6**; N=**2 772**; Moore bound=6826;
Graph obtained from the generailized hexagon *H*_{4} by replacement
of some of its vertices by complete graphs *K*_{4} using the same technique than
in reference (4,6)
G. Pineda-Villavicencio, J. Gómez, M. Miller, H. Pérez-Rosés.
New largest graphs of diameter 6. Electronic Notes in Discrete Mathematics
24 (2006) 153-160.

**H_5(K_4)**
Delta= **6**, Diam= **6**; N=**7917**; Moore bound=23437;
Graph obtained from the generailized hexagon *H*_{5} by replacement
of some of its vertices by complete graphs *K*_{4} using the same technique than
in reference (4,6)
G. Pineda-Villavicencio, J. Gómez, M. Miller, H. Pérez-Rosés.
New largest graphs of diameter 6. Electronic Notes in Discrete Mathematics
24 (2006) 153-160.

** Loz_11988**
Degree= **7**, Diameter =**6**; Order =11988; Moore bound=65318.
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.

**H_7(K_5)**
Delta= **8**, Diam= **6**; N=**39 672**; Moore bound=156865;
Graph obtained from the generailized hexagon *H*_{7} by replacement
of some of its vertices by complete graphs *K*_{5} using the same technique than
in reference (4,6)
J. Gómez. On large (D,6)-graphs.
*Networks* **46** (2005), pp. 82-87.
doi:10.1002/net.20075 .

**H_8(K_6)**
Delta= **9**, Diam= **6**; N=**75 893**; Moore bound=337042;
Graph obtained from the generailized hexagon *H*_{8} by replacement
of some of its vertices by complete graphs *K*_{6} using the same technique than
in reference (4,6)
G. Pineda-Villavicencio, J. Gómez, M. Miller, H. Pérez-Rosés.
New largest graphs of diameter 6. Electronic Notes in Discrete Mathematics
24 (2006) 153-160.

**H_9(K_6)**
Delta= **10**, Diam= **6**; N=**134 690**; Moore bound=664301;
Graph obtained from the generailized hexagon *H*_{9} by replacement
of some of its vertices by complete graphs *K*_{6} using the same technique than
in reference (4,6)
J. Gómez. On large (D,6)-graphs.
*Networks* **46** (2005), pp. 82-87.
doi:10.1002/net.20075 .

**H_11(K_8)**
Delta= **12**, Diam= **6**; N=**359 772**; Moore bound=2125873;
Graph obtained from the generailized hexagon *H*_{11} by replacement
of some of its vertices by complete graphs *K*_{8} using the same technique than
in reference (4,6)
G. Pineda-Villavicencio, J. Gómez, M. Miller, H. Pérez-Rosés.
New largest graphs of diameter 6. Electronic Notes in Discrete Mathematics
24 (2006) 153-160.

**H_13(K_11)**
Delta= **14**, Diam= **6**; N=**818 094**; Moore bound=;
Graph obtained from the generailized hexagon *H*_{13} by replacement
of some of its vertices by complete graphs *K*_{11} using the same technique than
in reference (4,6)
G. Pineda-Villavicencio, J. Gómez, M. Miller, H. Pérez-Rosés.
New largest graphs of diameter 6. Electronic Notes in Discrete Mathematics
24 (2006) 153-160.