New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts

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.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-30
DOI
https://doi.org/10.5281/zenodo.23788454
Primary Topic
Finite Group Theory Research
Type
preprint
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preprint

New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts

Rishabh Rajiv
Zenodo (CERN European Organization for Nuclear Research)
Finite Group Theory Research
preprint

New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts

Rishabh Rajiv
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Finite Group Theory Research
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New lower bounds for the degree-diameter problem from Cayley graphs of metacyclic groups, slack filling and chart lifts — Rishabh Rajiv · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS