Cospectral digraphs from locally line digraphs

A digraph Γ=(V,E) is a line digraph when every pair of vertices u,v∈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 Γ is a locally line digraph. In this paper we give a new method to obtain a...

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Bibliographic Details
Published in:Linear algebra and its applications 2016-07, Vol.500, p.52-62
Main Authors: Dalfó, C., Fiol, M.A.
Format: Article
Language:English
Subjects:
05 Combinatorics
05C Graph theory
Adjacency matrix
Classificació AMS
Cospectral digraph
De Bruijn digraph
Diameter
Digraph
Directed graphs
Grafs, Teoria de
Kautz digraph
Matemàtiques i estadística
Spectral theory (Mathematics)
Spectrum
Teoria espectral (Matemàtica)
Àrees temàtiques de la UPC
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Summary:A digraph Γ=(V,E) is a line digraph when every pair of vertices u,v∈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 Γ is a locally line digraph. In this paper we give a new method to obtain a digraph Γ′ cospectral with a given locally line digraph Γ with diameter D, where the diameter D′ of Γ′ 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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.03.014