On the coset graph construction of distance-regular graphs
Minjia Shi, Denis S. Krotov, Patrick Sol\'e
TL;DR
This paper demonstrates that the coset graph construction cannot produce new distance-regular graphs beyond those already cataloged in existing tables, confirming the completeness of known classifications.
Contribution
It proves the limitations of coset graph constructions for additive completely regular codes over finite fields in generating new distance-regular graphs.
Findings
No new distance-regular graphs can be obtained from coset graphs of additive codes.
The existing tables of distance-regular graphs are complete with respect to this construction.
The coset graph method does not extend the known catalog of such graphs.
Abstract
We show that no more new distance-regular graphs in the tables of the book of (Brouwer, Cohen, Neumaier, 1989) can be produced by using the coset graph of additive completely regular codes over finite fields.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems