Horst Sachs: On the Spectrum of a (3,6)-Cage
The chemistry of carbon cages (fullerenes) and related compounds has aroused
much interest in the spectral theory of embedded graphs (polyhedra).
A (p,q)-cage is (the graph of) a simple (i.e., trivalent) polyhedron each
which is a p-gon or a q-gon. (5,6)-cages correspond to the spherical
(3,6)-cages are closely related to the toroidal fullerenes (trivalent
tessellations of the torus), their structure can easily and intuitively be
by only three parameters (see ).
In the talk, the spectrum of a (3,6)-cage, including a central open problem
(P.W. Fowler's conjecture, see , p. 159), will be discussed.
 P.W. Fowler, P.E. John and H.Sachs,(3,6)-cages, hexagonal toroidal
and their spectra. DIMACS Series in Discrete Mathematics and Theoretical
Computer Science, Vol. 51 (2000), 139-174.