Directed Graphs of Frobenius Companion Matrices of Order 2

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Hamza A Daoub

Abstract

In this work, we explore the set of Frobenius companion matrices with entries from the ring of integers modulo a prime $p$, denoted as $M_2^{(F)}(\mathbb{Z}_p)$. We introduce a mapping $\psi$ to construct a directed graph $G_p$, where vertices represent these matrices and edges are defined by $\psi$. The study focuses on the structure and properties of $G_p$, including vertex degrees, cycles, and connected components, in relation to the eigenvalues of the matrices.

Article Details

How to Cite
Daoub, H. A. (2024). Directed Graphs of Frobenius Companion Matrices of Order 2. University of Zawia Journal of Natural Sciences, 1(1), 28–32. https://doi.org/10.26629/uzjns.v1i1.200
Section
Mathematics

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