Largest Known (Degree, Diameter)-Graphs (Description)

Largest Known (Degree, Diameter)-Graphs

Diameter 10

Last modification: June 22, 2025.

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

Delta= 3, Diam= 10; N=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.

Results for diameter 10 and degrees 5 to 16 obtained by Eyal Loz and Jozef Širáň ( New record graphs in the degree-diameter problem. Australas. J. Combin. 41 (2008), 63-80. ) except for entries with maximum degree 8,12, 14 and 16 found by Dharunish Yugeswardeenoo (dharyugi@gmail.com; August 2026), details coming soon.