TY - UNPB
T1 - Strongly regular graphs with parameters (85,14,3,2) do not exist
AU - Shpectorov, Sergey
AU - Zhao, Tianxiao
PY - 2025/4/3
Y1 - 2025/4/3
N2 - 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 srg(85, 14, 3, 2) exists.
AB - 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 srg(85, 14, 3, 2) exists.
U2 - 10.48550/arXiv.2504.02449
DO - 10.48550/arXiv.2504.02449
M3 - Preprint
BT - Strongly regular graphs with parameters (85,14,3,2) do not exist
PB - arXiv
ER -