Cospectral digraphs from locally line digraphs
C. Dalf\'o, M.A. Fiol

TL;DR
This paper introduces a new method to construct cospectral digraphs from locally line digraphs, preserving key properties and diameter within a small range, with applications to well-known digraph families.
Contribution
A novel technique for generating cospectral digraphs from locally line digraphs that maintains diameter and algebraic properties, extending the class of known cospectral constructions.
Findings
Constructed cospectral digraphs with diameter in [D-1,D+1]
Applied method to De Bruijn and Kautz digraphs
Preserved algebraic properties of original digraphs
Abstract
A digraph is a line digraph when every pair of vertices 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 is a locally line digraph. In this paper we give a new method to obtain a digraph cospectral with a given locally line digraph with diameter , where the diameter of is in the interval . 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.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Advanced Combinatorial Mathematics
