Computer generation of spectra of graphs: Applications to C60 clusters and other systems

A computer code based on the Givens–Householder matrix diagonalization method is used to calculate the spectra of graphs containing a large number of vertices. The code is most general in that it can handle graphs containing 200 or more vertices. Further, the code can be used to generate the spectra of weighted graphs. The program requires as input only the neighborhood table of the graph. The spectra of many graphs are generated for the first time in less than a few minutes of computer time. Applications to a number of chemical systems including two forms (foot and hand) of the recently synthesized C₆₀ cluster and the effect of bond alternation on these systems are discussed. In addition, the spectra of square and honeycomb lattices and the characteristic polynomials of the foot and hand forms of the C₆₀ cluster are obtained.