Strongly regular graphs from orthogonal groups O⁺(6,2) and O^-(6,2)

2016/09/22 by Dean Crnković, Crnković, Dean, Sanja Rukavina +3 · 1 citation
Computer Science · Engineering · Mathematics · #05E18 #05E30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05E18 #msc:05E30

paper · pdf · doi:10.48550/arxiv.1609.07133

14 pages, some remarks added to the first version

openalex publication_date 2016/09/22 · openalex created_date 2016/10/07 · arxiv created 2016/12/03 · arxiv updated 2016/12/06 · openalex updated_date 2026/07/28

Abstract

In this paper we construct all strongly regular graphs, with at most 600 vertices, admitting a transitive action of the orthogonal group O⁺(6,2) or O^-(6,2). Consequently, we prove the existence of strongly regular graphs with parameters (216,40,4,8) and (540,187,58,68). We also construct a strongly regular graph with parameters (540,224,88,96) that was to the best of our knowledge previously unknown. Further, we show that under certain conditions an orbit matrix M of a strongly regular graph Γ can be used to define a new strongly regular graph \widetildeΓ, where the vertices of the graph \widetildeΓ correspond to the orbits of Γ (the rows of M). We show that some of the obtained graphs are related to each other in a way that one can be constructed from an orbit matrix of the other.

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