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 )