Strongly regular graphs with parameters (85,14,3,2) do not exist
Abstract
We investigate the second smallest unresolved feasible set of parameters of strongly regular graphs, $(v,k,λ,μ)=(85,14,3,2)$. Using the classification of cubic graphs of small degree, we restrict possible local structure of such a graph $G$. After that, we exhaustively enumerate possible neighbourhoods of a maximal $3$-clique of $G$ and check them against a variety of conditions, including the combinatorial ones, coming from $λ=3$ and $μ=2$, as well as the linear algebra ones, utilising the Euclidean representation of $G$. These conditions yield contradiction in all cases, and hence, no $\mathrm{srg}(85,14,3,2)$ exists.
Fields of Study & Subjects
Finite Group Theory Research
graph theory and CDMA systems
Coding theory and cryptography
Publication details
- Journal / source
- Journal of Combinatorial Theory Series A
- Publisher
- Elsevier BV
- Volume
- 225
- Pages
- 106242–106242
- Publication date
- 30 July 2026
- Language
- EN