G-2007-72
Bounds on the Index of the Signless Laplacian of a Graph
, , , and BibTeX reference
Let be a simple, undirected graph of order
and size
with vertex set
, edge set
, adjacency matrix
and vertex degrees
.
The average degree of the neighbor of vertex
is
.
Let
be the diagonal matrix of degrees of
.
Then
is the Laplacian matrix of
and
the signless Laplacian matrix of
.
Let
denote the index of
and
the index of
.
We survey upper bounds on
and
given in terms of the
and
, as well as of the numbers of common neighbors of pairs of vertices.
It is well known that
.
We show that many but not all upper bounds on
are still valid for
.
Published September 2007 , 14 pages
This cahier was revised in April 2008
Research Axis
Research applications
Publication
Jan 2010
Bounds on the index of the signless Laplacian of a graph
, , , and
Discrete Applied Mathematics, 158(4), 355–360, 2010
BibTeX reference