Few Non-derogatory Directed Graphs from Directed Cycles

TL;DR

This paper constructs specific non-derogatory directed graphs by augmenting directed cycles, analyzing their characteristic polynomials and exponents to understand their algebraic properties.

Contribution

It introduces a method to generate non-derogatory digraphs from directed cycles and computes their spectral characteristics.

Findings

Identified classes of non-derogatory digraphs

Computed characteristic polynomials for these graphs

Analyzed their exponents and algebraic properties

Abstract

We constructed a few non-derogatory digraphs by adding arcs to a directed cycle and computed their characteristic polynomials and exponents.