p−Role Assignment for Cayley Graph Hℓ,p - Araújo, Athos J. de; Candia, Paulo F.; Ribeiro, André da Cunha (Anais do Encontro de Teoria da Computação (ETC); 2026: Anais do XI Encontro de Teoria da ComputaçãoDO - 10.5753/etc.2026.23602, 2026)
We study the role assignment problem in the family of Cayley graphs H ℓ,p . We show that there exists a natural graph homomorphism from H ℓ,p to a circulant graph Γ, which implies that every graph in this family admits a p-role assignment. We also present an efficient algorithm to compute such assignments in O(ℓp ℓ−1 ) time. Our results highlight the interplay between algebraic structure and role assignments in highly symmetric graphs.