Dot-product graphs in finite fields

Chengfei Xie; Gennian Ge

Dot-product graphs in finite fields

Combinatorics 2025-11-05 v1 Number Theory

Authors: Chengfei Xie , Gennian Ge

Abstract

In this paper, we study the dot-product graphs in $\mathbb{F}_q^d$ . We prove that if the size of the product of two adjacent sets is large enough, then the set of dot-product graphs has positive density. Our method is based on finite field Fourier analytic techniques.

Keywords

additive number theory tensor product graph theory

Cite

@article{arxiv.2511.02313,
  title  = {Dot-product graphs in finite fields},
  author = {Chengfei Xie and Gennian Ge},
  journal= {arXiv preprint arXiv:2511.02313},
  year   = {2025}
}

Comments

26 pages; any comments are welcome

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