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 H3 by replacement of some of its vertices (see figure) by complete graphs K3
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 H4 by replacement of some of its vertices by complete graphs K4 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 H5 by replacement of some of its vertices by complete graphs K4 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 H7 by replacement of some of its vertices by complete graphs K5 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 H8 by replacement of some of its vertices by complete graphs K6 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 H9 by replacement of some of its vertices by complete graphs K6 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 H11 by replacement of some of its vertices by complete graphs K8 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 H13 by replacement of some of its vertices by complete graphs K11 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.