Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique

2023/06/14 by Alexander L. Gavrilyuk, Gavrilyuk, Alexander L., V. V. Kabanov +1 · 1 citation
Mathematics · Chemistry · Biochemistry, Genetics and Molecular Biology · #Finite Group Theory Research #Ferrocene Chemistry and Applications #Chromatin Remodeling and Cancer

paper · pdf · doi:10.48550/arxiv.2306.08369

Abstract

In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph Sp(2d,q). In this paper, we determine the parameters of strongly regular graphs which admit a decomposition into a divisible design graph and a coclique attaining the Hoffman bound. In particular, it is shown that when the least eigenvalue of such a strongly regular graph is a prime power, its parameters coincide with those of the complement of Sp(2d,q). Furthermore, a generalization of the construction is discussed.

Cited by

• Thin divisible designs graphs: an interplay between fixed-point free involutions of (v,k,λ)-graphs and symmetric weighing matrices

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