There is no strongly regular graph with parameters (460,153,32,60)
A. V. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska
TL;DR
This paper proves the non-existence of a strongly regular graph with specific parameters using bounds on 4-cliques and Euclidean representations, advancing the understanding of SRG parameter constraints.
Contribution
It introduces a novel proof technique combining clique bounds and Euclidean representations to rule out certain SRG parameters.
Findings
No strongly regular graph exists with parameters (460,153,32,60)
New lower bounds on 4-cliques in SRGs established
Application of Euclidean representation methods to SRG non-existence proofs
Abstract
We prove that there is no strongly regular graph (SRG) with parameters (460,153,32,60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs.
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Taxonomy
TopicsFinite Group Theory Research · Limits and Structures in Graph Theory · Graph theory and applications