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24 June 2024
 
  » arxiv » 2302.00199

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Adjacency matrices over a finite prime field and their direct sum decompositions
Akihiro Higashitani ; Yuya Sugishita ;
Date 1 Feb 2023
AbstractIn this paper, we discuss the adjacency matrices of finite undirected simple graphs over a finite prime field $mathbb{F}_p$. We apply symmetric (row and column) elementary transformations to the adjacency matrix over $mathbb{F}_p$ in order to get a direct sum decomposition by other adjacency matrices. In this paper, we give a complete description of the direct sum decomposition of the adjacency matrix of any graph over $mathbb{F}_p$ for any odd prime $p$. Our key tool is quadratic residues of $mathbb{F}_p$.
Source arXiv, 2302.00199
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