Paley-like graphs over finite fields from vector spaces |
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Affiliation: | 1. School of Mathematics, South China University of Technology, Guangzhou, 510641, China;2. School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China;1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China;2. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China;3. Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China;4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;5. School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China;1. Dipartimento di Matematica, Università degli studi di Trento, Italy;2. College of Science, National University of Defense Technology, Changsha, 410073, China |
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Abstract: | Motivated by the well-known Paley graphs over finite fields and their generalizations, in this paper we explore a natural multiplicative-additive analogue of such graphs arising from vector spaces over finite fields. Namely, if and is an -vector space, is the (undirected) graph with vertex set and edge set . We describe the structure of an arbitrary maximal clique in and provide bounds on the clique number of . In particular, we compute the largest possible value of for arbitrary q and n. Moreover, we obtain the exact value of when is any -vector space of dimension . |
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Keywords: | Finite fields Paley graphs Sum-product estimates Bilinear forms |
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