**Abstract:** Linear damped wave equation on finite metric graphs is considered and its
asymptotical spectral properties are researched. In the case of linear
damped wave equation on an abscissa there is one high frequency abscissa,
one sequence of eigenvalues with real part approaching to a constant value.
In the case of a graph the location of high frequency abscissas can be
determined only by the averages of the damping function on each edge. For a
graph with equilateral edges we find lower and upper bounds on the number of
high frequency abscissas depending on the number of its edges and its
structure.

This is a joint work with prof. Pedro Freitas.