Largest Known (Degree, Diameter)-Graphs
Diameter 9
Last modification: June 22, 2025.
http://www-mat.upc.es/grup_de_grafs/desc_g9.html
raw adjacency list format: the first vertex of each row is adjacent to all the other vertices in that row.
implicit adjacency list format: each row corresponds to a vertex (row 1, vertex 0; row 2, vertex 1; and so on) and contains all vertices adjacent to it.
adjacency list NX NetworkX format. NetworkX format.
Exoo_600
Degree= 3, Diameter = 9; Order =600;
Moore bound=1534.
Voltage graph.
Download the implicit adjacency list of the graph.
This SageMath script computes several properties of the graphs including symmetry group sizes and the number of k-cycles (k=3..). This is the online version
Loz_7575
Degree= 4, Diameter = 9; Order =7575;
Moore bound=39365.
Communicated by Eyal Loz, Math Dep., Auckland Univ., New Zealand (July 2006)
Download the raw adjacency list of the graph.
Link to Eyal Loz's data. (eloz002 @ math .auckland. ac. nz )
Communicated July 2006.
Rod_331387
Degree= 6, Diameter = 9; Order =331 387;
Moore bound=2 929 686
nodes: 331387
edges: 994161
min deg: 6 max deg: 6
diameter: 9
avg. dist: 7.758922
Communicated by Alexis Rodriguez-Eduardo Canale. Instituto de Matematica y Estadistica / Facultad de Ingenieria - UDeLaR / Universidad de la Republica / Uruguay (August 20 2012)
El grafo con 331387 nodos con diametro 9 y grado 6, los parametros del grupo fueron: m = 6763, n = 49 y r = 41.
El cociente es B(0, 3) con los voltajes: (1254, 25), (541, 18) y (4642, 47)
Rodríguez de los Santos, A. (2013.).
Búsquedas masivas de grafos de gran orden con grado y diámetro acotados. Tesis de maestría. Universidad de la República (Uruguay). Facultad de Ingeniera.
Download the implicit adjacency list of the graph (13.6 MB).
Results for diameter 9 and degrees 7 to 16 obtained by Eyal Loz and Jozef Širáň.
New record graphs in the degree-diameter problem. Australas. J. Combin. 41 (2008), 63–80.