A digraph $\Gamma$ is called $n$-Cayley digraph over a group $G$, if there exists a semiregular subgroup $R_G$ of Aut$(\Gamma)$ isomorphic to $G$ with $n$ orbits. In this paper, we represent the adjacency matrix of $\Gamma$ as a diagonal block matrix in terms of irreducible representations of $G$ and determine its characteristic polynomial. As corollaries of this result we find: the spectrum of semi-Cayley graphs over abelian groups, a relation between the characteristic polynomial of an $n$-Cayley graph and its complement, and the spectrum of Calye graphs over groups with cyclic subgroups. Finally we determine the eigenspace of $n$-Cayley digraphs and their main eigenvalues.
@article{10_37236_3105,
author = {Majid Arezoomand and Bijan Taeri},
title = {On the characteristic polynomial of {\(n\)-Cayley} digraphs},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/3105},
zbl = {1295.05139},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3105/}
}
TY - JOUR
AU - Majid Arezoomand
AU - Bijan Taeri
TI - On the characteristic polynomial of \(n\)-Cayley digraphs
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/3105/
DO - 10.37236/3105
ID - 10_37236_3105
ER -
%0 Journal Article
%A Majid Arezoomand
%A Bijan Taeri
%T On the characteristic polynomial of \(n\)-Cayley digraphs
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/3105/
%R 10.37236/3105
%F 10_37236_3105
Majid Arezoomand; Bijan Taeri. On the characteristic polynomial of \(n\)-Cayley digraphs. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/3105
