Spectra of Digraph Transformations
Combinatorics
2017-07-04 v1
Abstract
For a digraph D and three parameters x, y, z in {0,1,+,-} we define the digraph D^(x,y,z) and call it the (x,y,z)-transformation of D. We show that for every r-regular digraph D the adjacency characteristic polynomial A(t, D^(x,y,z)) of (x,y,z)-transformation of D is uniquely defined by r and the adjacency characteristic polynomial A(t, D) of digraph D and we give a description of this function A(t, D^(x,y,z)) = F(r, A(t, D)). We also obtain similar results for some non-regular digraphs, namely, for so-called digraph-functions and their inverse. Also using the (x,y,z)-transformations of digraphs, we give various new constructions of non-isomorphic adjacency cospectral digraphs.
Cite
@article{arxiv.1707.00401,
title = {Spectra of Digraph Transformations},
author = {Aiping Deng and Alexander Kelmans},
journal= {arXiv preprint arXiv:1707.00401},
year = {2017}
}