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Abstract
Given simple graphs and
, the neighbourhood corona of
and
, denoted
, is the graph obtained by taking one copy of
and
copies of
, and joining the neighbours of the
th vertex of
to every vertex in the
th copy of
. In this paper we determine the adjacency spectrum of
for arbitrary
and
, and the Laplacian spectrum and signless Laplacian spectrum of
for regular
and arbitrary
, in terms of the corresponding spectrum of
and
. The results on the adjacency and signless Laplacian spectra enable us to construct new pairs of adjacency cospectral and signless Laplacian cospectral graphs. As applications of the results on the Laplacian spectra, we give constructions of new families of expander graphs from known ones by using neighbourhood coronae.
AMS Subject Classification:
Acknowledgements
We appreciate the anonymous referees for their comments and suggestions. X. Liu is supported by MIFRS and MIRS of the University of Melbourne. S. Zhou is supported by a Future Fellowship (FT110100629) of the Australian Research Council.