Yuya Sugishita | Searcharxiv

arXiv2023

Adjacency matrices over a finite prime field and their direct sum decompositions

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 $\mathbb{F}_p$.

math.CO↗

arXiv2022

A characteristic polynomial of the Seidel matrix over $\mathbb{F}_3$

In this paper, we consider the condition when the characteristic polynomials of the Seidel matrix of the graphs are decomposed into products of linear polynomials over $\mathbb{F}_3$. We also show the equality over $\mathbb{F}_3$ between the characteristic polynomial of the Seidel matrix of a graph and the characteristic polynomial of the adjacency matrix of that graph.

math.CO↗