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
face of
which is a p-gon or a q-gon. (5,6)-cages correspond to the spherical
fullerenes;
(3,6)-cages are closely related to the toroidal fullerenes (trivalent
hexagonal
tessellations of the torus), their structure can easily and intuitively be
described
by only three parameters (see [1]).
In the talk, the spectrum of a (3,6)-cage, including a central open problem
(P.W. Fowler's conjecture, see [1], p. 159), will be discussed.
[1] P.W. Fowler, P.E. John and H.Sachs,(3,6)-cages, hexagonal toroidal
cages,
and their spectra. DIMACS Series in Discrete Mathematics and Theoretical
Computer Science, Vol. 51 (2000), 139-174.