Can I read Adjacency Matrices Over a Finite Prime Field and Their Direct Sum Decompositions on EtoBox?

Adjacency Matrices Over a Finite Prime Field and Their Direct Sum Decompositions by Higashitani, Akihiro; Sugishita, Yuya is a scholarly article available to read on EtoBox.

What is Adjacency Matrices Over a Finite Prime Field and Their Direct Sum Decompositions about?

In 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 $\mathbb{F}_p$.

Author

Higashitani, Akihiro; Sugishita, Yuya

Published

2023

Language

EN