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arXiv · 1707.00401

Spectra of Digraph Transformations

Aiping Deng·Alexander Kelmans
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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.

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Aiping Deng, Alexander Kelmans. 2017-07-03. Spectra of Digraph Transformations. https://arxiv.org/abs/1707.00401

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