ABSTRACT
Let G be a simple graph of order n with m edges. Denote by the diagonal matrix of its vertex degrees and by
its adjacency matrix. Then the signless Laplacian matrix of G is
. Let
be the signless Laplacian eigenvalues of graph G and also let
be the largest positive integer such that
. Denote by
the complement graph of graph G. If
, then we prove that
. Moreover, if
, then
.
AMS CLASSIFICATION:
Acknowledgements
The author would like to thank the referee for his/her valuable comments which lead to an improvement of the original manuscript.
Disclosure statement
No potential conflict of interest was reported by the author.