New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts
Year: 2026
Type: preprint
Abstract: We give 21 new lower bounds for the degree-diameter problem with degree d ≤ 20 and diameter k ≤ 10, from 20 explicit graphs. Of these, 15 are Cayley graphs of semidirect products of two cyclic groups, at diameters 8, 9 and 10, the largest with 120 461 699 776 vertices at (d, k) = (19, 10); the other 5 are obtained by filling the spare degree of known graphs, and by lifts of small controller graphs through charts over finite fields. The constructions are known; the graphs are new. Every graph is given explicitly, in the paper or in the accompanying dataset, and verified by breadth-first search.
Author: Rajiv, Rishabh
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224916455