Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets |
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Institution: | 1. Faculty of Education, Kumamoto University, 2-40-1 Kurokami, Kumamoto 860-8555, Japan;2. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
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Abstract: | In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters. |
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Keywords: | Affine polar graph Quadratic form Singer difference set Strongly regular graph Subdifference set |
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