Csíkvári Péter:
Graph polynomials and graph generating functions
<br><br>
In the talk we will study some analytic properties of the so-called
independence polynomial and the adjoint polynomial. Concerning the
independence polynomial we will give a new proof for the fact that it has 
a
unique root of smallest modulus which is real. In case of the adjoint
polynomial we will prove that its root having the largest absolute value 
is
real and it is at most 4(D-1), where $D$ is the largest degree. This bound
is sharp. In the first half of the talk I will try to explain the 
connection
of these results with extremal graph theory and statistical physics.