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:
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;
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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.