IIMAS - FENOMEC
UNAM
Exploring soft graphs
por el
Resumen:
We are interested in graphs whose
graph laplacian have an eigenvector
with a null component. These null components play an
important role when
the graph Laplacian is used to describe miscible flows on a
network.
On these null components, any action, control
or observation of the system is impossible; because they are
so
important it is useful to detect them in general networks.
The graph laplacian is the matrix of node degrees minus the
adjacency matrix : we refer to [3] for definitions and
results on graph spectra. In a previous work [1] we called
{\it soft node} a vertex corresponding to such a component.
In the case of a multiple eigenvalue, any component of an
eigenvector may be zero and we call {\it absolute soft node}
a vertex with value zero for all eigenvector in the
subspace.
Here we call $\lambda$-{\it soft graphs} graphs with a soft
node for
an eigenvalue $\lambda$. We present a classification [2] of
$\lambda$-soft
graphs containing up to 6 nodes, as well as some particular
classes of graphs,
sorted by value of $\lambda$.
This shows a structure within each $\lambda$-soft set with
transformations connecting its members. This
suggests that we can build soft graphs and find eigenvectors
with soft
nodes combinatorially.
Informes: coloquiomym@gmail.com, o al 5622-3564.