Cospectral digraphs from locally line digraphs

A digraph Gamma = (V, E) is a line digraph when every pair of vertices u, v is an element of V have either equal or disjoint in -neighborhoods. When this condition only applies for vertices in a given subset (with at least two elements), we say that Gamma is a locally line digraph. In this paper we give a new method to obtain a digraph Gamma' cospectral with a given locally line digraph Gamma with diameter D, where the diameter D' of Gamma' is in the interval [D - 1, D + 1]. In particular, when the method is applied to De Bruijn or Kautz digraphs, we obtain cospectral digraphs with the same algebraic properties that characterize the formers. (C) 2016 Elsevier Inc. All rights reserved.