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Abstract
Let and
be two simple graphs. Denote the corona and the edge corona of
and
by
and
, respectively. In this paper, first, the normalized Laplacian spectrum of
is given in terms of that of
and
when both
and
are regular. Then the normalized Laplacian spectrum of
is given in terms of that of
and
for any connected graph
and a regular graph
. Finally, as applications, the number of spanning trees and the degree Kirchhoff index of
and
are considered.
AMS Subject Classifications:
Acknowledgements
The authors would like to express their sincere gratitude to the referees for a very careful reading of this paper and for their valuable suggestions, which led to an improvement of the original manuscript.
Notes
No potential conflict of interest was reported by the authors.