Largest Known (Degree, Diameter)-Graphs

Diameter 10

Last modification: August 27, 2026.
http://www-mat.upc.es/grup_de_grafs/desc_g10.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.
Conder_1250
Degree = 3, Diameter = 10; Order =1 250; Moore bound=3070;
Communicated by Marston Conder ( m.conder@auckland.ac.nz ) on August 17, 2006. http://www.math.auckland.ac.nz/~conder/symmcubic2048list.txt
Marston Conder, Jicheng Ma. Arc-transitive abelian regular covers of cubic graphs. J. Algebra, 387 (2013) 215-242.
Download the raw adjacency list of the graph.
Download the adjacency list (NetworkX) of the graph.
This SageMath script computes several properties of the graph including symmetry group sizes and the number of k-cycles (k=3..). This is the online version .
Dahr_18369
Degree= 4, Diameter = 10; Order =18369; Moore bound=118097.
Dharunish Yugeswardeenoo (dharyugi@gmail.com; August 17, 2026). Results obtained by using a hybrid discovery framework in development: LLM-guided search over classical algebraic constructions, combined with local search and exact completion. The specific LLMs used were OpenAI's Sol 5.6 and Anthropic's Claude Fable 5 Max. Voltage lift of a 3-vertex base multigraph over the semidirect group Z_157 (x9) Z_397. Order: 18369 / Size: 36738 / 4-reg.? True / Girth: 12 / Diam.: 10 / Avg.dist: 8.17560 / Aut.group.ord.: 6123 / Automorphism group structure C157 x| C39
This SageMath online script computes several properties of the graph including symmetry group sizes (run it locally).
Download the raw adjacency list .

Former result, order = 17703
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.
Rajiv_1253751
Degree= 6, Diameter =10; Order = 1253751; Moore bound = 14648436
Obtained by Rishabh Rajiv (rishabh.rajiv@alumni.ubc.ca, August 24, 2026) with the use of AI agentic coding systems.
Cayley graph of the semidirect group Z43 (⋊4) Z29157, with generators Avg.dist: 8.61308186. Dist. distrib. : [ 1, 6, 30, 150, 750, 3750, 18622, 89010, 355526, 661676, 124230].
In this link you can download the adjacency list, a verifier (standard-library Python), and a paper describing the construction of the graph.
Dahr_24914017
Degree= 8, Diameter = 10; Order =24914017; Moore bound= 376633664
Dharunish Yugeswardeenoo (dharyugi@gmail.com; August 17, 2026). Results obtained by using a hybrid discovery framework in development: LLM-guided search over classical algebraic constructions, combined with local search and exact completion. The specific LLMs used were OpenAI's Sol 5.6 and Anthropic's Claude Fable 5 Max.
Cayley graph of the semidirect group Z67 (⋊193531) Z371851, with generators (63, 153081) (4, 296486) (51, 188360) (16, 328020) (10, 284948) (57, 202073) (35, 287031) (32, 231598) Avg.dist: 8.81099198. Dist. distrib. :[ 1, 8, 56, 392, 2744, 19198, 133638, 909884, 5450434, 15342166, 3055496]
Results for diameter 10 and degrees 5, 7, 9, 11, 13 and 15 obtained by Eyal Loz and Jozef Širáň ( New record graphs in the degree-diameter problem. Australas. J. Combin. 41 (2008), 63-€“80. ) Entries for diameter 8 and degrees 8,12, 14 and 16 found by Dharunish Yugeswardeenoo (dharyugi@gmail.com; August 2026).