On Cayley Graphs of Skew Braces and Their Distances

We introduce the left and right Cayley graphs of a finite skew brace (A,·, ∘) with a connection set T⊂ A, as a directed multigraph with additive and multiplicative edges, depicting the operations · and ∘ respectively. We compute the distance from a to a∘ b in these Cayley graphs in terms of factorization lengths over T. As an application, we provide a characterization of the ideals of a skew brace in terms of their corresponding Cayley graphs.