2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75829A unitary equivalence class of endomorphisms of a unital C$^{*}$-algebra ${\cal A}$ is called a {\it sector} of ${\cal A}$. We introduced permutative endomorphisms of the Cuntz algebra ${\cal O}_N$ in the previous work. Branching laws of permutative representations of ${\cal O}_N$ by them are computed by directed regular graphs. In this article, we classify sectors associated with permutative endomorphisms of ${\cal O}_N$ by their graph invariants concretely.Operator Algebras47D25text